数列{an}满足a1=1,a(n+1)=an/(an+1),令bn=1/an,证明{bn}为等差数列
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![数列{an}满足a1=1,a(n+1)=an/(an+1),令bn=1/an,证明{bn}为等差数列](/uploads/image/z/8633052-36-2.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%3D1%2Ca%28n%2B1%29%3Dan%2F%28an%2B1%29%2C%E4%BB%A4bn%3D1%2Fan%2C%E8%AF%81%E6%98%8E%7Bbn%7D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97)
数列{an}满足a1=1,a(n+1)=an/(an+1),令bn=1/an,证明{bn}为等差数列
数列{an}满足a1=1,a(n+1)=an/(an+1),令bn=1/an,证明{bn}为等差数列
数列{an}满足a1=1,a(n+1)=an/(an+1),令bn=1/an,证明{bn}为等差数列
a(n+1)=an/(an+1)
∴1/a(n+1)=(an+1)/an=1+1/an
∵bn=1/an
∴b(n+1)=1+bn
∴﹛bn﹜是等差数列
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