等差数列的题目等差数列an中,各项均不为0 求证(1/a1a2)+(1/a3a4）+（1/a5a6）+、、、、、、+（1

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+1/a3-1/a4+…………+1/an-1/a(n+1)]
=(1/d)[1/a1-1/a(n+1)]
=(1/d)[a(n+1)-a1]/[a1*a(n+1)]
=(1/d)*nd*/[a1*a(n+1)]
=n/[a1*a(n+1)]
希望楼主以后提问能多核对几次题目,这样的误写会让题目面目全非,成为没有答案的无头题目,