1/3*2/5+1/5*2/7+ 1/7*2/9+……+1/99*2/101

问题描述:

1/3*2/5+1/5*2/7+ 1/7*2/9+……+1/99*2/101
怎样简便计算?

1/3×2/5=1/3-1/5同理1/5×2/7=1/5-1/7后面类推得:所以原式=1/3 × 2/5+1/5 ×2/7+1/7 ×2/9+……1/99 × 2/101=(1/3-1/5)+(1/5-1/7)+……+(1/99-1/101)=1/3-1/101=98/303 ∵每一项都是1/(2n+1)×2/(2n+3)的形式,n...