# What is the radius of convergence of the series P∞ n=0 x n ? Let r be the radius of convergence from question

(a) What is the radius of convergence of the series P∞ n=0 x n ? Let r be the radius of convergence from question (a).

(b) Find a closed form expression for the series P∞ n=0 x n assuming |x| < r. In other words, find a function f(x) that returns the value of the series using only a finite number of operations. Note: f(x) = P∞ n=0 x n is not a closed form expression since it involves an infinite number of operations. (c) Find a closed form expression for the series P∞ n=1 x n assuming |x| < r. (d) Find a closed form expression for the series P∞ n=m x n assuming |x| < r, where m ≥ 0.

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