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Given the function: $$f(x) =\frac{(11+x)}{(1-x)}$$ how would I find a power series representation? I started by rewriting the function as $$(11+x)\frac{(1)}{(1-x)}$$ and then arrived at $$(11+x)\sum_{i=0}^\infty x^n$$ But I am not sure how I would pull the x into the summation.

Derek
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1 Answers1

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$$(11 + x) \sum_{n=0}^\infty x^n = 11 \sum_{n=0}^\infty x^n + x \sum_{n=0}^\infty x^n = \sum_{n=0}^\infty 11 x^n + \sum_{n=1}^\infty x^n = 11 + \sum_{n=1}^\infty 11 x^n + \sum_{n=1}^\infty x^n = 11 + \sum_{n=1}^\infty 12 x^n $$

Claude
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