To find: Interval of convergence and sum as a function of x for the given series.
Answer to Problem 26E
Interval of convergence is
Explanation of Solution
Given:
The series given is,
Calculation:
A series is convergence when the limit of partial sum tends to infinity i.e.
Also, common ratio should be less than one i.e.
Now, the given series is
Here, the above series is geometric series having common ratio
So,
i.e. the interval of convergence is
Now, determining the sum of the geometric series.
Here in
So, sum is
Therefore, interval of convergence is
Chapter 10 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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