lim[n/(n^2+1^2)+n/(n2+2^2)+···n/(n^2+n^2)] n->无穷大
1个回答
n/(n^2+i^2) = (1/n)/(1+(i/n)^2)
所以原式 = ∫(0,1) 1/(1+x^2)dx = arctanx|(0,1)=π/4
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