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  • To: mathgroup at smc.vnet.net
  • Subject: [mg27996] Sums
  • From: Janusz Kawczak <jkawczak at math.uncc.edu>
  • Date: Wed, 28 Mar 2001 02:40:24 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello:

can anybody help? I am trying to evaluate the following:

Sum[n (1-r)^(IntegerPart[n/k]) Boole[ 0 < r < .5], {n, 1, Infinity}],
for some k >1, but fixed.

In the same fashion, many other sums are of interest:

Sum[n (n+1) (1-r)^(IntegerPart[n/k]) Boole[ 0 < r < .5], {n, 1,
Infinity}],
for some k >1, but fixed, and so on.

Also, the finite sums are of some interest to me as well, i.e.

Sum[n (1-r)^(IntegerPart[n/k]) Boole[ 0 < r < .5], {n, 1, N}],
for some k >1, but fixed.

The above sum can be easily evaluated without the IntegerPart in
the exponent. But, I cannot get it to work in general.

Any help with this matter will be greatly appreciated.
John.

P.S. Please cc to jkawczak at math.uncc.edu.



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