1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900
问题描述：
1/6+1/12+1/20+1/30+1/42+1/56+.+1/9900
答
1/6+1/12+1/20+1/30+1/42+1/56+...+1/9900
=1/(2×3)+1/(3×4)+1/(4×5)+1/(5×6)+1/(6×7)+1/(7×8)+...+1/(99×100)
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+...+1/99-1/100
=1/2-1/100
=49/100