用数学计算证明:
在调和级数中,∑1/n-lnn≈c,c是它们之间的差值,也就是它们之间的差值,应该只能这个常数的左右,最大也是不能越过一的。
要记住的是:∑1/n-lnn≈c,这是一个约等于,所以说,它也不是标准值,只是一个近似值。近似值以近似值之间,是不能相互否定的,只能看谁最接近标准值。
在欧拉那个年代,科技水平决定了他们不可能搞出来,调和级数的标准公式来,所以,只能采用近似的方法,来计算它的和值。用近似的方法就只能采用常数。
实际上这个所谓的常数,是一个驱近于零的数值,下面用数学计算证明:
.....N.........................∑............................lnn..............................标准的变化数值
....1......................1.00000.......................0......................................1.00000
.....2.....................1.50000...................0.67932................................0.80285
.....3.....................1.83333...................1.09861................................0.73472
.....4.....................2.83333...................1.38629................................0.69704
.....5.....................2.28333....................1.60944...............................0.67389
.....6.....................2.45000....................1.79176................................0.65824
.....7.....................2.59286.....................1.94591...............................0.64695
.....8.....................2.71786.....................2.07944...............................0.63842
.....9.....................2.82897.....................2.19722...............................0.63275
....10....................2.92897.....................2.30259...............................0.62638
.....20...................3.59774.....................2.99573...............................0.60201
.....30...................3.99499.....................3.40120...............................0.59379
.....40...................4.27854......................3.68888..............................0.58966
.....50...................4.49921......................3.91202..............................0.58719
.....60...................4.67987......................4.09435..............................0.58719
.....70...................4.83284......................4.24850..............................0.58434
.....80...................4.96548......................4.38203..............................0.58345
.....90...................5.08257......................4.49981..............................0.58276
....100..................5.18738......................4.60517...............................0.58221
.....200.................5.87803......................5.29831...............................0.57972
.....300.................6.28266......................5.70378...............................0.57888
.....400.................6.56993......................5.99146...............................0.57847
.....500.................6.79282......................6.21460...............................0.57822
.....600.................6.97498......................6.39693...............................0.57805
.....700.................7.12901......................6.55108...............................0.57793
.....800.................7.26245......................6.68461...............................0.57784
.....900.................7.38017......................6.80240...............................0.57777
....1000................7.48547......................6.90776...............................0.57771
....2000................8.17837......................7.60092...............................0.57745
....3000...............8.58375.......................8.00637...............................0.57738
.......N.........................∑...........................lnn...........................变化常数
....4000..................8.87075.................8.29405......................0.57670
....5000..................9.09342.................8.51719......................0.57623
....6000..................9.27515.................8.69952......................0.57563
....7000..................9.42882.................8.85367......................0.57515
....8000..................9.56196.................8.98719.......................0.57487
....9000..................9.67958.................9.10498.......................0.57460
....一万...................9.78467.................9.21034.......................0.57433
....二万..................10.47584................9.90349.......................0.57235
....三万..................10.87719...............10.30895......................0.56824
....四万..................11.16213...............10.59663......................0.56550
....五万..................11.38340...............10.81978......................0.56362
....六万..................11.56438...............11.00210......................0.56228
...七万...................11.71740...............11.15625......................0.56115
...八万...................11.85016...............11.28978......................0.56036
...九万...................11.96733...............11.40757......................0.55976
...十万...................12.07219...............11.51293......................0.55926
..二十万................12.76336...............12.20678......................0.55658
..三十万................13.16471...............12.61154......................0.55317
..四十万................13.44965...............12.89922......................0.55043
..五十万................13.67092...............13.12236......................0.54856
..六十万................13.85190...............13.30469......................0.54721
..七十万................14.00502...............13.45884......................0.54618
..八十万................14.13778...............13.59237......................0.54541
..九十万.................14.25495..............13.71015......................0.54480
...百万...................14.35981...............13.81551......................0.54430
..二百万................15.05098................14.50866.....................0.54232
..三百万................15.45233................14.91412.....................0.53821
..四百万................15.73727................15.20181.....................0.53546
.....N..................................∑..................................lnn................................变化常数
..二亿亿兆..................74.42497........................74.37587..........................0.04910
..三亿亿兆..................74.82520........................74.78134..........................0.04386
..四亿亿兆..................75.10958........................75.06902..........................0.04056
..五亿亿兆..................75.33051........................75.29216..........................0.03835
..六亿亿兆..................75.51126........................75.47448..........................0.03678
..七亿亿兆..................75.66424........................75.62833..........................0.03591
..八亿亿兆..................75.79687........................75.76217..........................0.03470
..九亿亿兆..................75.91393........................75.98531..........................0.03399
..十亿亿兆..................76.01871........................75.98531..........................0.03340
..二十兆兆..................76.70713........................76.67846..........................0.02567
..三十兆兆..................77.10737........................77.08392..........................0.02345
..四十兆兆..................77.39175........................77.37160..........................0.02016
..五十兆兆..................77.61268........................77.59475..........................0.01793
.六十兆兆...................77.79343........................77.77707..........................0.01536
.七十兆兆..................77.94641.........................77.93122..........................0.01519
.八十兆兆..................78.07904.........................78.06496..........................0.01408
.九十兆兆..................78.19610.........................78.18253..........................0.01357
.百亿亿兆..................78.30088.........................78.28787..........................0.01299
.二百兆兆..................78.98830.........................78.98104..........................0.00726
.三百兆兆..................79.38859.........................79.28651..........................0.00208
.四百兆兆..................79.67297.........................79.67419..........................0.00000
数学计算充分证明,这个所谓的常数,是由一,不断的走向零的。
当:∑1/n-lnn=0,就收敛了,因为不能出现负增值,∑1/n≈79.67297。
正确的就是正确的,你们越是拼命的耍流氓,越是证明你们内心害怕,反过来越是证明就是正确!
正确的理论,就一定要坚定和坚信到底!
在调和级数中,∑1/n-lnn≈c,c是它们之间的差值,也就是它们之间的差值,应该只能这个常数的左右,最大也是不能越过一的。
要记住的是:∑1/n-lnn≈c,这是一个约等于,所以说,它也不是标准值,只是一个近似值。近似值以近似值之间,是不能相互否定的,只能看谁最接近标准值。
在欧拉那个年代,科技水平决定了他们不可能搞出来,调和级数的标准公式来,所以,只能采用近似的方法,来计算它的和值。用近似的方法就只能采用常数。
实际上这个所谓的常数,是一个驱近于零的数值,下面用数学计算证明:
.....N.........................∑............................lnn..............................标准的变化数值
....1......................1.00000.......................0......................................1.00000
.....2.....................1.50000...................0.67932................................0.80285
.....3.....................1.83333...................1.09861................................0.73472
.....4.....................2.83333...................1.38629................................0.69704
.....5.....................2.28333....................1.60944...............................0.67389
.....6.....................2.45000....................1.79176................................0.65824
.....7.....................2.59286.....................1.94591...............................0.64695
.....8.....................2.71786.....................2.07944...............................0.63842
.....9.....................2.82897.....................2.19722...............................0.63275
....10....................2.92897.....................2.30259...............................0.62638
.....20...................3.59774.....................2.99573...............................0.60201
.....30...................3.99499.....................3.40120...............................0.59379
.....40...................4.27854......................3.68888..............................0.58966
.....50...................4.49921......................3.91202..............................0.58719
.....60...................4.67987......................4.09435..............................0.58719
.....70...................4.83284......................4.24850..............................0.58434
.....80...................4.96548......................4.38203..............................0.58345
.....90...................5.08257......................4.49981..............................0.58276
....100..................5.18738......................4.60517...............................0.58221
.....200.................5.87803......................5.29831...............................0.57972
.....300.................6.28266......................5.70378...............................0.57888
.....400.................6.56993......................5.99146...............................0.57847
.....500.................6.79282......................6.21460...............................0.57822
.....600.................6.97498......................6.39693...............................0.57805
.....700.................7.12901......................6.55108...............................0.57793
.....800.................7.26245......................6.68461...............................0.57784
.....900.................7.38017......................6.80240...............................0.57777
....1000................7.48547......................6.90776...............................0.57771
....2000................8.17837......................7.60092...............................0.57745
....3000...............8.58375.......................8.00637...............................0.57738
.......N.........................∑...........................lnn...........................变化常数
....4000..................8.87075.................8.29405......................0.57670
....5000..................9.09342.................8.51719......................0.57623
....6000..................9.27515.................8.69952......................0.57563
....7000..................9.42882.................8.85367......................0.57515
....8000..................9.56196.................8.98719.......................0.57487
....9000..................9.67958.................9.10498.......................0.57460
....一万...................9.78467.................9.21034.......................0.57433
....二万..................10.47584................9.90349.......................0.57235
....三万..................10.87719...............10.30895......................0.56824
....四万..................11.16213...............10.59663......................0.56550
....五万..................11.38340...............10.81978......................0.56362
....六万..................11.56438...............11.00210......................0.56228
...七万...................11.71740...............11.15625......................0.56115
...八万...................11.85016...............11.28978......................0.56036
...九万...................11.96733...............11.40757......................0.55976
...十万...................12.07219...............11.51293......................0.55926
..二十万................12.76336...............12.20678......................0.55658
..三十万................13.16471...............12.61154......................0.55317
..四十万................13.44965...............12.89922......................0.55043
..五十万................13.67092...............13.12236......................0.54856
..六十万................13.85190...............13.30469......................0.54721
..七十万................14.00502...............13.45884......................0.54618
..八十万................14.13778...............13.59237......................0.54541
..九十万.................14.25495..............13.71015......................0.54480
...百万...................14.35981...............13.81551......................0.54430
..二百万................15.05098................14.50866.....................0.54232
..三百万................15.45233................14.91412.....................0.53821
..四百万................15.73727................15.20181.....................0.53546
.....N..................................∑..................................lnn................................变化常数
..二亿亿兆..................74.42497........................74.37587..........................0.04910
..三亿亿兆..................74.82520........................74.78134..........................0.04386
..四亿亿兆..................75.10958........................75.06902..........................0.04056
..五亿亿兆..................75.33051........................75.29216..........................0.03835
..六亿亿兆..................75.51126........................75.47448..........................0.03678
..七亿亿兆..................75.66424........................75.62833..........................0.03591
..八亿亿兆..................75.79687........................75.76217..........................0.03470
..九亿亿兆..................75.91393........................75.98531..........................0.03399
..十亿亿兆..................76.01871........................75.98531..........................0.03340
..二十兆兆..................76.70713........................76.67846..........................0.02567
..三十兆兆..................77.10737........................77.08392..........................0.02345
..四十兆兆..................77.39175........................77.37160..........................0.02016
..五十兆兆..................77.61268........................77.59475..........................0.01793
.六十兆兆...................77.79343........................77.77707..........................0.01536
.七十兆兆..................77.94641.........................77.93122..........................0.01519
.八十兆兆..................78.07904.........................78.06496..........................0.01408
.九十兆兆..................78.19610.........................78.18253..........................0.01357
.百亿亿兆..................78.30088.........................78.28787..........................0.01299
.二百兆兆..................78.98830.........................78.98104..........................0.00726
.三百兆兆..................79.38859.........................79.28651..........................0.00208
.四百兆兆..................79.67297.........................79.67419..........................0.00000
数学计算充分证明,这个所谓的常数,是由一,不断的走向零的。
当:∑1/n-lnn=0,就收敛了,因为不能出现负增值,∑1/n≈79.67297。
正确的就是正确的,你们越是拼命的耍流氓,越是证明你们内心害怕,反过来越是证明就是正确!
正确的理论,就一定要坚定和坚信到底!