[seqfan] Re: Question about limit of 1/(k*Pi(k))

[Olivier Gerard]

On Thu, Jan 8, 2015 at 5:10 PM, Bob Selcoe <rselcoe at entouchonline.net>
wrote:

> Hello Seqfans,
>
> Is the following true, and if so, a known property?
>
> Where Pi(k) is the k-th prime and k = 1..inf:
>
> Sum_(1/(k*Pi(k))) = 1
>
> i.e., 1/2 + 1/6 + 1/15 + 1/28 + 1/55...
>

No, this is not true, by a significant margin.

This sum is strictly inferior to

Sum_(1/(k*(k+1)))  which is equal to 1.


Olivier