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。求过程

因为1/（1*3）=1/2*(1/1-1/3)分解2=3-1=5-3=7-5=-=101-99所以 1/1＊3+1/3＊5+1/5＊7+-+1/99＊101 =1/2(2/1＊3+2/3＊5++-+2/99＊101) =1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101) =1/2(1-1/101) =50/101

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