To find: First three nonzero term, general term and interval of convergence of the given function.
Answer to Problem 11E
The first three nonzero terms are,
The general term is,
And the interval of convergence is
Explanation of Solution
Given:
The given function is,
Calculation:
As,
The Maclaurin series of
So, Maclaurin series of
So, Maclaurin series of
Hence, the first three term are,
And the general term of the series is
Now, for determining the interval of convergence use ration test. So,
So, the series will converge if
Now checking the convergence at the end points.
Put
It is a series of infinite sum so it diverges.
Put
This series also diverges since it never approaches to zero
So, the series converges if
Hence, the interval of convergence is
Chapter 10 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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