MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Problem with a limit.


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.


  • Prev by Date: Derivative[1] applied to numeric constants
  • Next by Date: Re: Adding a notebook (or folder) to the Mathematica Front End menus?
  • Previous by thread: Re: Derivative[1] applied to numeric constants
  • Next by thread: Re: Problem with a limit.