3/(1^2*2^2)+5/(2^2*3^2)+``````+(2n+1)/(n^2*(n+1)^2)的极限怎么求

题目

3/(1^2*2^2)+5/(2^2*3^2)+``````+(2n+1)/(n^2*(n+1)^2)的极限怎么求

答案

(2n+1) / [ n²(n+1)² ] = 1/n² - 1/(n+1)²
∴原式 = 1 - 1/(n+1)²
极限为 1
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