Question

一乘三分之一加三乘五分之一加五乘七分之一加······加九十七乘一百零一分之一,等于多少.

Answer 1

1/(1×3) + 1/(3×5) + 1/(5×7) + …… + 1/(99×101)

= (1/2)×( 1 - 1/3 )+ (1/2)×(1/3 - 1/5) + (1/2)×(1/5 - 1/7) + …… + (1/2)×(1/99 - 1/101)

= (1/2)×( 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + …… + 1/99 - 1/101)

= (1/2)×( 1 - 1/101)

= (1/2)×(100/101)

= 50/101