lim[x→无穷][1/(1×3)+1/(3×5)+.+1/(2n-1)×(2n+1)]
问题描述：
lim[x→无穷][1/(1×3)+1/(3×5)+.+1/(2n-1)×(2n+1)]
答
=1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+.1/2*(1/(2n-1)-1/(2n+1))
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-.+1/(2n-1)-1/(2n+1))
=1/2*(1-1/(2n+1))=1/2 when n goes to infinity.