Problem with a limit.

*To*: mathgroup at smc.vnet.net*Subject*: [mg66759] Problem with a limit.*From*: Roger Bagula <rlbagulatftn at yahoo.com>*Date*: Mon, 29 May 2006 06:05:51 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

This sum works really well: a = Sum[(PrimePi[k + 1] - PrimePi[k])/2^k, {k, 1, Infinity}] I got the idea to look at it from the other end as primes dominate the low end of the Integers: Limit[Sum[(PrimePi[k + 1] - PrimePi[k])/2^(n - k), {k, 1, n}], n -> Infinity] So I tried: Table[N[Limit[Sum[(PrimePi[ k + 1] - PrimePi[k])/2^(n - k), {k, 1, n}], n ->10^m], {m, 1, 10}] It's just an interesting problem in how the primes are distributed.

**Follow-Ups**:**Re: Problem with a limit.***From:*danl@wolfram.com