1/(1×3)+1/(3×5)+1/(5×7)+.+1/(2n-1)(2n+1)等于多少?

问题描述:

1/(1×3)+1/(3×5)+1/(5×7)+.+1/(2n-1)(2n+1)等于多少?

=1/2(1-1/3+1/3-1/5+…… +1/(2n-1)-1/(2n+1))
1/2(1-1/(2n+1))=n/2n+1