已知数列｛an｝满足a1=2,a(n+1)=2an/(an+2),证明：数列｛1/an｝为等差数列
人气：313 ℃ 时间：2020-01-28 02:58:56
解答
a(n+1)=2an/(an+2),a1=2,说明an>0∵a(n+1)=2an/(an+2),∴1/a(n+1)=(an+2)/2an=1/an+1/2∴1/a(n+1)-1/an=1/2,a1=2所以｛1/an｝为等差数列
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