你的题目写错了,要求证的应该是[1/(a1a2)]+[1/(a2a3)]+[1/(a3a4)]+…………+[1/(an*a(n+1))]证明：设公差为d,则1/[an*a(n+1)]=(1/d)[a(n+1)-an]/[an*a(n+1)]=(1/d)[1/an-1/a(n+1)]∴原式=(1/d)[1/a1-1/a2+1/a2-1/a3+...