Let a n = (1 + 1/n)n. (a) Show that if 0 a < b, then
Question:
Let an = (1 + 1/n)n.
(a) Show that if 0 ≤ a < b, then
(b) Deduce that bn[(n + 1)a − nb], an+1.
(c) Use a = 1 + 1/(n + 1) and b = 1 + 1/n in part (b) to show that {an} is increasing.
(d) Use a = 1 and b = 1 + 1/(2n) in part (b) to show that a2n < 4.
(e) Use parts (c) and (d) to show that an < 4 for all n.
(f) Use Theorem 12 to show that limn→∞(1 + 1/n)n exists.
Transcribed Image Text:
b"+l - a"+1 a*+1 b — а < (п + 1)b"
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a b Since b a 0 we have c Substituting in part d Substituting ...View the full answer
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Related Book For
Calculus Early Transcendentals
ISBN: 9781337613927
9th Edition
Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin
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