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 + + + ^{ ... } + + ^{ ... } |