a1=2 an+1/an=n/n+1 求an 为什么数列{nan}是各项均等于2的常数数列.a(n+1)/an=n/(n+1 )
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a1=2an+1/an=n/n+1求an为什么数列{nan}是各项均等于2的常数数列.a(n+1)/an=n/(n+1)a1=2an+1/an=n/n+1求an为什么数列{nan}是各项均等于2的常数
a1=2 an+1/an=n/n+1 求an 为什么数列{nan}是各项均等于2的常数数列.a(n+1)/an=n/(n+1 )
a1=2 an+1/an=n/n+1 求an 为什么数列{nan}是各项均等于2的常数数列.
a(n+1)/an=n/(n+1 )
a1=2 an+1/an=n/n+1 求an 为什么数列{nan}是各项均等于2的常数数列.a(n+1)/an=n/(n+1 )
把an移到右边,a(n+1)=(nan)/(n+1)
用n-1代入上式的n处,an=[(n-1)/n]*a(n-1)
=[(n-1)/n]*[(n-2)/(n-1)]*[(n-3)/(n-2)]*.*[(2-1)/2]*a(2-1)
=[(n-1)/n]*[(n-2)/(n-1)]*[(n-3)/(n-2)]*.*1/2*a1
=1/n*a1=a1/n=2/n
故nan=2
{nan}是各项均等于2的常数数列.
解析,
a(n+1)/an=n/(n+1),
[(n+1)*a(n+1)]/(an*n)=1,a1=2
得出,n*an=2。
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