Let an = (n), where is a continuous, decreasing function such that (x)

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Let an = ƒ (n), where ƒ is a continuous, decreasing function such that ƒ (x) ≥ 0 andS. f(x) dx.

Assume an converges to S. Arguing as in Exercise 81, show that n=1 Conclude that M n=1 M+1 Sme f(x) dx  5  [


Data From Exercise 81

Let an = ƒ (n), where ƒ is a continuous, decreasing function such that ƒ (x) ≥ 0 andS. f(x) dx.

Show that

Sf(x) dx s f(x) dx an  a + n=1 f f(x) f(x) dx


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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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