1/(2n-1)(2n+1)
=1/2*2/(2n-1)(2n+1)
=1/2*[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=1/2*[(2n+1)/(2n-1)(2n+1)-(2n-1)/(2n-1)(2n+1)]
=1/2*[1/(2n-1)-1/(2n+1)]
所以原式=1/2*[1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=n/(2n+1)这道提前面有给你一个规律，是：1/1x2=1-1/21/2x3=1/2-1/3 1/3x4=1/3-1/4……能否利用这个规律来解上题？就是这个