$\displaystyle \sum^{\infty}_{n=0} 1/(2+x)$ and $\displaystyle \sum^{\infty}_{n=0} x^3/(x+2)$ oops they arent the series, but the power series representation so ignore the sigmas
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BECAUSE $\displaystyle {x^3\over x+2}= x^3 \biggl({1\over 2+x}\biggr) = x^3 \biggl({1/2\over 1-(-x/2)}\biggr)$ Which is a geo with r=-x/2, which converges whenever |-x/2|<1 or -2<x<2.
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