倪举鹏 发表于 2014-2-14 18:45:56

质数倒数和问题

1/2^n+1/3^n+1/5^n+1/7^n+1/11^n……=S
这个n至少要多少 S才收敛？ 收敛成多少，是个特殊数么，n是特殊数么？

Lwins_G 发表于 2014-2-14 19:04:47

$n>1$时皆收敛。

wayne 发表于 2014-2-14 20:36:05

http://mathworld.wolfram.com/PrimeZetaFunction.html
{#, N, 20]} & /@ Range


{2,0.45224742004106549851},
{3,0.17476263929944353642},
{4,0.076993139764246844943},
{5,0.035755017483924257133},
{6,0.017070086850636512954},
{7,0.0082838328561335925351},
{8,0.0040614053665178305605},
{9,0.0020044675749624506631},
{10,0.00099360357443698021786}}
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