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Unformatted text preview: MAT 127: Calculus C
MiniQuiz:
Computing sums of inﬁnite series DO NOT TURN THIS PAGE OVER YET This miniquiz is for practice only. It will not be graded or even collected. On the next page, you will ﬁnd a problem containing four convergent inﬁnite series. You are asked
to explain why each of the series converges and to compute its sum. You have 30 minutes to complete the entire problem. The analogous problem on the ﬁnal will have only two parts. Taking about 20 minutes on it should
be ok (this would be one point per minute, which is what you need to average). Thus, you are
being asked to complete the miniquiz at a slightly higher pace than needed for the ﬁnal exam. Show that the following series are convergent and ﬁnd their sums.
∞ (a)
n=1 1
n2n ∞ (b)
n=1 ∞ (c)
n=0 ∞ (d)
n=0 n
2n (−1)n π 2n+1
42n+1 (2n +1)! (−1)n (ln 2)n
n! ...
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 Fall '07
 GuanYuShi
 Calculus

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