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2. Determine the values of x for which the given series converges absolutely, converges conditionally or diverges. Σ (x+3) 2

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Answer #1

Solution:

Given Go (x + 3) 2n yn +3 n=1 Applying ratio test for Σα, lim n00 an+1 an = lim n+00 (x + 3)1+1 2n+1/(n+1) + 3 (x + 3) 21 y

Thus ***|<1 -1<*73 <1 -2<x+3<2 -5 < x < -1 Thus the series converges within the interval (-5, -1]. For endpoints At x=-5 (x +

At x=-1 00 1 (x + 3) 2n n +3 = (2) 2vn+ 3 Vn+ 3 n=1 n=1 n=1

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