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.
You can write T = 1/(1 - r)^2.
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