Solution: In Exercises 7982, determine whether the statement is true or false. If it is
Chapter 9, Problem 82(choose chapter or problem)
True or False? In Exercises 79-82, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
If \(f(x)=\sum_{n=0}^{\infty} a_{n} x^{n}\) converges for |x| < 2, then \(\int_{0}^{1} f(x) d x=\sum_{n=0}^{\infty} \frac{a_{n}}{n+1}\).
Text Transcription:
f(x) = sum_n = 0 ^infty a_n x^n
int_0 ^1 f(x) dx = sum_n = 0 ^infty a_n / n + 1
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