求数列1/1×3,1/2×4,1/3×5,.,1/n(n＋2),的前n项和Sn
问题描述：
求数列1/1×3,1/2×4,1/3×5,.,1/n(n＋2),的前n项和Sn
答
裂项相消法.1/[n(n+2)]=1/2*[1/n-1/(n+2)] ,所以原式=1/2*[1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/(n-1)-1/(n+1)+1/n-1/(n+2)]=1/2*[1+1/2-1/(n+1)-1/(n+2)]=n(3n+5) / [4(n+1)(n+2)] ....