{an}为等差数列,an不等于0,d为公差,求证:1/(a1a2)+1/(a2a3)+...+1/(an-1*an)=(n-1)/(aian)
问题描述：
{an}为等差数列,an不等于0,d为公差,求证:1/(a1a2)+1/(a2a3)+...+1/(an-1*an)=(n-1)/(aian)
答
证明：
∵{an}为等差数列,an不等于0,d为公差
∴左边=1/a1-1/a2+1/a2-1/a3+...+1/（an-1）-1/an
=1/a1-1/an
=an/a1an-a1/a1an
=(an-a1)/a1an
=右边
感觉你后面打错了（n-1）？
答
证明：左边＝1/(a1a2)+1/(a2a3)+...+1/(an-1*an)＝1/d(1/a1-1/a2)+1/d(1/a2-1/a3)+...+1/d(1/an-1-1/an)=1/d[(1/a2-1/a1)+(1/a3-1/a2)+...+(1/an-1-1/an)]=1/d[1/a1+(1/a2-1/a2)+(1/a3-1/a3)+...+(1/an-1 - 1/an-1)-...