1+1/√2+1/√3+...+1/√n前面各项的值:
n=1->1
n=2->1.70711
n=3->2.28446
n=4->2.78446
n=5->3.23167
n=6->3.63992
n=7->4.01788
n=8->4.37144
n=9->4.70477
n=10->5.021
n=20->7.59526
n=30->9.58513
n=40->11.2676
n=50->12.7524
n=100->18.5896
n=500->43.2834
n=1000->61.801
n=5000->139.968
n=10000->198.545
n=100000->630.997
n=1000000->1998.54
n=10000000->6323.1
n=100000000->19998.5
n=1000000000->63244.1
n=10000000000->199999.
n=100000000000->632454.
这个求和在n->+∞时是发散的:
n->+∞->+∞
注:这个求和式叫做HarmonicNumber[n,1/2],
HarmonicNumber[n,k]=1/1^k+1/2^k+...+1/n^k
n->+∞:当k>1时,和为有限数,当k+∞