1/n(n+2)=1/2*[1/n-1/(n+2)]
所以1/1*3+1/2*4+1/3*5+1/4*6+...+1/n(n+2)
=1/2*[1-1/3+1/2-1/4+1/3-1/5+…+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)]
1/1*3+1/2*4+1/3*5+1/4*6+...+1/n(n+2)
=(1/2)*[1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+/15-1/7+....+1/n-1/(n+2)]
=(1/2)*[1+1/2-1/(n+1)-1/(n+2)]
=(1/2)*[3/2-(2n+3)/(n+1)(n+2)]
=3/4-(2n+3)/[2(n+1)(n+2)]
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