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Unformatted text preview: MAT 127: Calculus C
MiniQuiz:
approximating 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 two convergent inﬁnite series. You will need
to explain why each of them converges and to estimate the sum of each of them with speciﬁed
precision. You have 20 minutes to complete the entire problem. Taking about 10 minutes on the analogous oneseries problem on the ﬁnal 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 about the same pace as needed for the ﬁnal exam. Explain why each of the following series converges. Then estimate its sum to within 2−10 using the
minimal possible number of terms, justifying your estimate; leave your answer as a simple fraction
p/q for some integers p and q with no common factor. Is your estimate an under or overestimate
for the sum? Explain why.
∞ (a)
n=1 1
n5 ∞ (b)
n=1 (−1)n
n5 ...
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 Fall '07
 GuanYuShi
 Calculus

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