Problem : What is the radius of convergence of x^{n}? of (- 1)^{n}x^{n}?
Since the radius of convergence only has to do with absolute convergence, the answer to the two parts will be the same. Since x^{n} is a geometric series, it converges whenever x≤1, but does not converge when x = 1. Therefore, r = 1 is its radius of convergence.Problem : Using the fact that
e^{x} = 1 + x + + + ^{ ... } + + ^{ ... } |
e = 1 + 1 + + + ^{ ... } + + ^{ ... } |
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