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# This week in class, we covered one way to sum an arithmetico-geometric series. Now we're going to cover a different approach.

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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 a and r .

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

Feb 9, 2018
edited by waffles  Feb 10, 2018