高一等比数列的题1.a1=1,an+1=(n+1)an,求an.2.a1=1,an+1=3an+3∧n,求an.3.a1

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高一等比数列的题
1.a1=1,an+1=(n+1)an,求an.
2.a1=1,an+1=3an+3∧n,求an.
3.a1=1/2,an+1=an+1/2n,求an.

1.因为a(n+1)/an=n+1,所以an/a(n-1)*a(n-1)/a(n-2)*……a2/a1=n!,所以an=n!
2.在等式两边同时除以3^(n+1),则a(n+1)/3^(n+1)=an/3^n+1/3,即数列{an/3^n}成等差,所以an/3^n=(a1)/3+(n-1)/3=n/3,所以an=n*3^(n-1)
3.因为a(n+1)-an=(1/2)n,所以an-a(n-1)+a(n-1)-a(n-2)+……+a2-a1=1/2(n-1)+1/2(n-2)+……+1/2=（n-1)n/2,an=(1+n(n-1)）/2

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