Question

一道高数求极限的题目lim(n→无穷大)n/(n^2+3)+n/(n^2+12)+...+n/(n^2+3n^2)=答案

Answer 1

用定积分来做

把分母上提出个n^2,所以

原极限=lim1/n* ∑1/[(1+3(k/n)^2]

=∫[1/(1+3x^2)]dx 积分区间o到1

=1/√3 arctan√3x| (o到1)

=1/√3（π/3-0)

=√3·π/9