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Chapter 8: Q 28. (page 704)
Manipulating power series: Find power series representations
for the indicated functions.
The power series representations for the indicated functions
is
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If m is a positive integer, how can we find the Maclaurin series for the function if we already know the Maclaurin series for the function f(x)? How do you find the interval of convergence for the new series?
In Exercises 49鈥�56 find the Taylor series for the specified function and the given value of . Note: These are the same functions and values as in Exercises 41鈥�48.
Find the interval of convergence for each power series in Exercises 21鈥�48. If the interval of convergence is finite, be sure to analyze the convergence at the endpoints.
How may we find the Maclaurin series for f(x)g(x) if we already know the Maclaurin series for the functions f(x) and g(x)? How do you find the interval of convergence for the new series?
Prove that if is the interval of convergence for the series , then the series converges conditionally at .
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