1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
问题描述：
1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
答
裂项：
1/(1×4)=1/3(1-1/4)
1/(4×7)=1/3(1/4-1/7)
.
1/(25×28)=1/3(1/25-1/28)
∴1/1×4+1/4×7+1/7×10+...+1/22×25+1/25×28
=1/3[(1-1/4)+(1/4-1/7)+(1/7-1/10)+.+(1/22-1/25)+(1/25-1/28)]
=1/3[1-1/28]
=9/28