1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
问题描述：
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20
答
因为1/[n(n+2)]=1/2 × [(n+2)-n]/[n(n+2)]=1/2 × [1/n-1/(n+2)]所以1\1×3 + 1\2×4+ 1\3×5 …… +1\18×20=1/2×(1/1-1/3)+1/2×(1/2-1/4)+1/2×(1/3-1/5)+……+1/2×(1/18-1/20)=1/2×(1/1-1/3+1/2-1/4+1/3-1/5...