Question

If the power series sum_{n=1}^{infty }a_{n}: x^{n} converges uniformly in ]α, β[ then so does . sum_{n=1}^{infty }a_{n}: (-x)^{n}. True or false? Justify.

10 Apr 2022
Answer :
Word Count : 256
The statement is True. Here's the justification: We are given a power series of the form: \[ \sum_{n=1}^{\infty} a_n x^n \] and we are told that this series converges uniformly on the interval \( ]\alpha, \beta[ \). The task is to check ___ _________ ____ _______ ______.
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