赞 共回答了10个问题采纳率：90% 举报
1/1*3+1/2*4+…+1/(n(n+2))
=1/2*(1-1/3+1/2-1/4+1/3-1/5+.+1/n-1/(n+2))
=1/2*(1+1/2-1/(n+1)-1/(n+2))
=3/4-(n+3/2)/(n+1)(n+2)
所以原式=3/4-lim(x→∞)(n+3/2)/(n+1)(n+2)
=3/4-lim(x→∞)(1/n+3/2n^2)/(1+3/n+2/n^2)
=3/4
=1/2*(1-1/3+1/2-1/4+1/3-1/5+.+1/n-1/(n+2))
=1/2*(1+1/2-1/(n+1)-1/(n+2))
=3/4-(n+3/2)/(n+1)(n+2)
所以原式=3/4-lim(x→∞)(n+3/2)/(n+1)(n+2)
=3/4-lim(x→∞)(1/n+3/2n^2)/(1+3/n+2/n^2)
=3/4
1年前
5
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