An infinite product P = a 1 a 2 a 3 . . , which is denoted

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An infinite product P = a1 a2 a3 . . , which is denoted По ак k=1 is the limit of the sequence of partial products {a1, a1 a2, a1 a2 a3,  . . .}. Assume that ak > 0 for all k.

a. Show that the infinite product converges (which means its sequence of partial products converges) provided the series Σ In ak k=1 converges.

b. Consider the infinite product

Write out the first few terms of the sequence of partial products,

(for example, P2 = 3/4, P3 = 2/3). Write out enough terms to determine the value of

c. Use the results of parts (a) and (b) to evaluate the series 

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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