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

[Jack Brennen]

Here's your sum:

    http://oeis.org/A124012

Or 0.848969034043...

- Jack


On 1/8/2015 9:11 AM, Olivier Gerard wrote:
> 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
>
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