①已知数列{an}满足a1=1,an+1=an/3an+1,求证数列{1/an}是等差数列②sn=1+x²+...+x的(n-1)次方.
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①已知数列{an}满足a1=1,an+1=an/3an+1,求证数列{1/an}是等差数列②sn=1+x²+...+x的(n-1)次方.①已知数列{an}满足a1=1,an+1=an/3an
①已知数列{an}满足a1=1,an+1=an/3an+1,求证数列{1/an}是等差数列②sn=1+x²+...+x的(n-1)次方.
①已知数列{an}满足a1=1,an+1=an/3an+1,求证数列{1/an}是等差数列②sn=1+x²+...+x的(n-1)次方.
①已知数列{an}满足a1=1,an+1=an/3an+1,求证数列{1/an}是等差数列②sn=1+x²+...+x的(n-1)次方.
an+1=an/3an+1,
两边取倒数
1/a(n+1)=(3an +1)/an =3+1/an
1/a(n+1)-1/an=3
所以 {1/an}是等差数列,首项为1/a1=1,公差为3
1/an=1+3(n-1)
1/an=3n-2
所以 an=1/(3n-2)
(2)等比数列求和公式即可
① x=1 ,Sn=1+2+3+...+n=n(n+1)/2
② x≠1,Sn=(1-x^n)/(1-x)
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