裂项法: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+…+1/n-1/(n+2)】=1/2*【1+1/2-1/(n+1)-1/(n+2)】