这个式子裂项相消怎么做

2025-06-20 15:13:41
推荐回答(1个)
回答1:

Tn=(1/2)[1-1/3+1/2-1/4+1/3-1/5+...+1/(n+3)-1/(n-1)+1/(n-2)-1/n+1/(n-1)-1/(n+1)+1/n-1/(n+2)]
=(1/2)[1+1/2-1/(n+1)-1/(n+2)],【正负相抵后前面剩余1+1/2,后面剩余-1/(n+1)-1/(n+2)】
=(1/2)[3/2-(2n+3)/[(n+1)(n+2)],
=3/4-(2n+3)/[2(n+1)(n+2)],