设数列an的前n项和为Sn,已知S1=1,Sn+1/Sn=n+c/n,且a1,a2,a3成等差数列

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设数列an的前n项和为Sn,已知S1=1,Sn+1/Sn=n+c/n,且a1,a2,a3成等差数列
设数列an的前n项和为Sn,已知S1=1,S（n+1）/Sn=（n+c）/n,且a1,a2,a3成等差数列
求：
1、求c的值
2、求数列an的通项公式
3、求人解答

1.s2/s1=c+1 s2=c+1 a2=c s3/s2=(2+c)/2 s3=(2+c)(c+1)/2 a3=c(c+1)/2
2a2=a1+a3 2c=1+ c(c+1)/2 c^2-3c+2=0 c=1或2
2.c=1时 s(n+1)/sn=(n+1)/n sn/s(n-1)=n/(n-1)…… 叠乘可知sn/s1=n
sn=n an=1
c=2时 s(n+1)=(n+2)/n sn/s(n-1)=(n+1)/(n-1) s(n-1)/s(n-2)=n/(n-2)……
sn/s1=n(n+1)/1*2 sn=n(n+1)/2 an=n

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