To find: First three nonzero term, general term and interval of convergence of the given function.
Answer to Problem 7E
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 Maclaurin series of
So for Maclaurin series of
So, the series is
O, the first three nonzero terms 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 alternating harmonic series so it converges.
Put
It is also alternating harmonic series so it converges.
So, the series converges when
Hence, the interval of convergence is
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic
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