Let (a) Show that ln(n + 1) S n 1 + ln n. (b) Show

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Let


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(a) Show that ln(n + 1) ≤ Sn ≤ 1 + ln n.


(b) Show that the sequence {an} = {Sn - ln n} is bounded.


(c) Show that the sequence {an} is decreasing.


(d) Show that the sequence {an} converges to a limit ϒ (called Euler’s constant).


(e) Approximate ϒ using a100.

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Calculus Of A Single Variable

ISBN: 9781337275361

11th Edition

Authors: Ron Larson, Bruce H. Edwards

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