数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!

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数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!数列

数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!
数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!

数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.要详解答案,我采纳!急用!
a(n+1)/an=n/(n+1),用累乘的方法求an.
a2/a1=1/2
a3/a2=2/3
a4/a3=3/4,继续写……
an/a(n-1)=(n-1)/n
把这些乘起来,得:
an/a1=1/n,即得:
an=1/n.

an+1/an=n/n+1
所以an+1=an+1/an*an/an-1*……*a2/a1*a1=n/n+1*n-1/n*……*1/2*1=1/n+1
所以an=1/n (n>1) an=1 (n=1)

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