计算 1/(1*3)+1/(3*5)+1/(5*7)+...+1/(2N-1)*(2N-1)=?

问题描述:

计算 1/(1*3)+1/(3*5)+1/(5*7)+...+1/(2N-1)*(2N-1)=?

=1/2*[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=n/(2n+1)