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.

T = r/(1 - r)^3.