若数列{an}为各项均不为零的等差数列,那么1/a1a2+1/a2+a3+1/a3a4+...+1/anan+1的和是什
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若数列{an}为各项均不为零的等差数列,那么1/a1a2+1/a2+a3+1/a3a4+...+1/anan+1的和是什么
![若数列{an}为各项均不为零的等差数列,那么1/a1a2+1/a2+a3+1/a3a4+...+1/anan+1的和是什](/uploads/image/z/18468415-55-5.jpg?t=%E8%8B%A5%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%BA%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%8D%E4%B8%BA%E9%9B%B6%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E9%82%A3%E4%B9%881%2Fa1a2%2B1%2Fa2%2Ba3%2B1%2Fa3a4%2B...%2B1%2Fanan%2B1%E7%9A%84%E5%92%8C%E6%98%AF%E4%BB%80)
1/anan+1=1/d(1/an-1/an+1)
1/a1a2+1/a2+a3+1/a3a4+...+1/anan+1
=1/d(1/a1-1/a2+1/a2-1/a2+...+1/an-1/an+1)
=1/d(1/a1-1/an+1)
这是裂项相消法求和
1/a1a2+1/a2+a3+1/a3a4+...+1/anan+1
=1/d(1/a1-1/a2+1/a2-1/a2+...+1/an-1/an+1)
=1/d(1/a1-1/an+1)
这是裂项相消法求和
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