Re: Problem with a limit.

*To*: mathgroup at smc.vnet.net*Subject*: [mg66779] Re: Problem with a limit.*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 30 May 2006 05:48:21 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e5ei0n$7to$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Roger Bagula wrote: > 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. > Hi Roger, I am not sure what the question is, since the sum returned unevaluated and the last command -- Table[xxx] -- returns a couple of error messages. Perhaps you can try In[2]:= Table[N[Sum[(PrimePi[k + 1] - PrimePi[k])/ 2^(10^n - k), {k, 1, 10^n}]], {n, 1, 5}] Out[2]= -9 {1.08398, 1.06275, 0.0634804, 3.7835 10 , 0.0012207} I hope I have not missed the point. Best regards, Jean-Marc