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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Question

Written 8 Q1

V12(-1)"
3" (2n + 1)
V12(-1)"
3" (2n + 1)
Consider the series
Note: this was changed from
n=0
n=1
Use any test for convergence/divergence to show that the series converges.
V12(-1)"
(b)
It is possible to show that the sum of the series
is T,
in other words, the series
3" (2n + 1)
n=0
converges to the number T. (You do NOT need to prove this, but it can be done somewhat easily using a
Taylor series expansion of arctan x.)
Suppose you want to use a partial sum of this series to estimate the value of T to an accuracy of within
0.0001. Would using the first 8 terms of the series be enough to ensure you get an accuracy of within
0.0001? (8 terms means the terms where n = 0, 1,2, 3, ....., 7.)
Note: This was changed from "7 terms".
Hint: Use Theorem 5.14.

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