证明:1/1*2*3+1/2*3*4+……1/n*(n+1)*(n+2)
问题描述:
证明:1/1*2*3+1/2*3*4+……1/n*(n+1)*(n+2)
答
裂项:
1/n*(n+1)*(n+2)=1/2*【1/n*(n+1)-1/(n+1)*(n+2)】
故1/1*2*3+1/2*3*4+……1/n*(n+1)*(n+2)
=1/2【1/1*2-1/2*3+1/2*3……+1/n(n+1)-1/(n+1)(n+2)】
=1/2【1/2-1/(n+1)(n+2)】
=1/4-1/2(n+1)(n+2)