数列求和1/1*3,1/2*4,1/3*5...1/n(n+2)

1/1*3=(1/2)(1-1/3)
1/2*4=(1/2)(1/2-1/4)
...
1/n(n+2)=(1/n - 1/(n+2))/2
原式=(1/2)(1-1/3+1/2-1/4+...+1/(n-1)-1/(n+1)+1/(n)-1/(n+2))
=(1/2)(1+1/2-1/(n+1)-1/(n+2))
=3/4-(2n+3)/2(n+1)(n+2)