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Unformatted text preview: [ 2 ] (F) Determine the radius of convergence of S ( x ) , and write down the interval of con-vergence of the series. Brieﬂy explain your reasoning. R = ∞ , interval of convergence = ( ∞ , ∞ )  We use the ratio test and consider ρ = lim n → ∞ | a n + 1 a n | with a n = x 2 n / n !. We ﬁnd that ρ = lim n → ∞ | x 2 n + 1 | = 0 regardless of the value of x . Since ρ < 1 for all values of x , the ratio test tells us that the series converges everywhere....
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This note was uploaded on 02/29/2012 for the course MATH 152 taught by Professor Sc during the Fall '08 term at Rutgers.
- Fall '08