Use the power series $\frac{1}{1+x} = \sum_{n=0}^{\infty} (-1)^n x^n$ to determine a power series, centered at 0, for the function. Identify the interval of convergence. 17) $h(x) = \frac{-2}{x^2 - 1} = \frac{1}{1+x} + \frac{1}{1-x}$ 18) $f(x) = -\frac{1}{(x+1)^2} = \frac{d}{dx} [\frac{1}{x+1}]$
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.. Now, we need to determine the interval of convergence for this power series. To do this, we can use the ratio test. The ratio test states that for a power series ∑(a_n*x^n), if the limit of |a_(n+1)/a_n| as n approaches infinity is L, then the series converges Show more…
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