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Let \(|r| < 1 \) ,

\(S = \sum_{k=0}^{\infty} r^k, \)
and 
\(T = \sum_{k=0}^{\infty} k r^k. \)
Our approach is to write T as a geometric series in terms of S and r.

Give a closed form expression for T in terms of r.

 May 29, 2020
 #1
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You can write T = 1/(1 - r)^2.

 Jul 5, 2020

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