1/1×3+1/3×5+1/5×7+......+1/【2n-1】【2n+1】

原式=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)

= 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)

0.5(1-1/3+1/3-1/5+…+
1/2n-1-1/2n+1)=0.5(1-
1/2n+1)

=（1/1-1/3+1/3-1/5+......+1/[2n-1]-1/[2n+1])/2
=(1/1-1/[2n+1])/2
=2n/[2n+1]/2
=n/[2n+1]

原式=0.5[1-1/3+1/3-1/5+1/5-…-1/(2n-1)
+1/(2n-1)-1/(2n+1)]=0.5[1-1/(2n+1)]=n/(2n+1)