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1. Given that 1 /1−x = ∞∑n=0 x^n with convergence in (−1, 1), find the power...

1. Given that 1 /1−x = ∞∑n=0 x^n with convergence in (−1, 1), find the power series for x/1−2x^3 with center 0.

∞∑n=0=

Identify its interval of convergence. The series is convergent from

x=
to x=

2. Use the root test to find the radius of convergence for
∞∑n=1 (n−1/9n+4)^n xn

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