tokelly
幼苗
共回答了10个问题采纳率:100% 举报
题错了,应为小于3/4;
前三项的和为63/120(1/3+1/8+1/15),已大于1/2.
Tn=1/(1*3)+1/(2*4)+1/(3*5)⋯⋯+1/(n(n+2))
=(1/2)(1/1-1/3)+(1/2)(1/2-1/4)+(1/2)(1/3-1/5)+⋯⋯+
(1/2)(1/n-1/(n+2))
=(1/2)(1/1-1/3+1/2-1/4+1/3-1/5+⋯⋯+1/n-1/(n+2))
=(1/2)(3/2-1/(n-2))
小于3/4
1年前
3