Consider the alternating series a. Write out the first ten terms of the series, group them in

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Consider the alternating series

4 if k is odd k + 1’ E(-1)*+'ak, where ap k=1 if k is even k'

a. Write out the first ten terms of the series, group them in pairs, and show that the even partial sums of the series form the (divergent) harmonic series.

b. Show that = 0. lim ak

c. Explain why the series diverges even though the terms of the series approach zero.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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