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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.

 
 Dec 4, 2021

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