Question

一乘三分之一加三乘五分之一加五乘七分之一加七乘九分之一加九乘十一 得多少

Answer 1

用裂项法：

原式

= 1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+1/(9×11)

= (1/2)(1-1/3)+(1/2)(1/3-1/5)+(1/2)(1/5-1/7)+(1/2)(1/7-1/9)+(1/2)(1/9-1/11)

= (1/2)[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]

= (1/2)(1-1/11)

= 5/11