- #1
Justabeginner
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Homework Statement
Find the interval of convergence for the following power series. Specify both absolute and conditional convergence where appropriate.
Homework Equations
1 + x + 2x^2 + 6x^3 + ... + n! x^n + ...
The Attempt at a Solution
Using the ratio test to determine convergence of the series, I have the following:
(n+1)! x^(n+1)/[n! x^n] = (n!)(x^(n+1))/[(n!)(x^n)]
= x(n+1) (After cancellation of factorials)
= x * lim n->∞ (n+1)
x < 1 converges
x > 1 diverges
Series does not converge?
I'm not sure if my answer is right or not. Any help is much appreciated. Thanks!