(2x+1)" n2 5. n=1 (> Answer (v Solution Use the ratio test : (2æ + 1)"+'/(n + 1)²| lim n2 lim n+00 n2 + 2n + 1 | 2x + 1| = |2x + 1|. |(2x + 1)"/n²| n00 Therefore the series converges absolutely for |2x +1|< 1, or |æ +1/2|< 1/2. The radius of convergence is p = 1/2. At x = 0 and x = -1, the series also converges absolutely.

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