用简便方法计算:1/30+1/42+1/56+...+1/2450=

Question

用简便方法计算:1/30+1/42+1/56+...+1/2450=

Answer 1

1/[n(n+1)]=(1/n)-[1/(n+1)]
∴原式
=1/5-1/6+1/6-1/7+…………+1/49-1/50
=1/5-1/50
=9/50
谢谢