等差数列{an}是递增数列,前n项和为Sn,且a1,a3,a9成等比数列,S5=(a5)^2 (1)求数列{an}的通项公式 (2)若数列{bn}满足bn=(n^2+n+1)/(an*an+1),求数列{bn}的前99项和
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![等差数列{an}是递增数列,前n项和为Sn,且a1,a3,a9成等比数列,S5=(a5)^2 (1)求数列{an}的通项公式 (2)若数列{bn}满足bn=(n^2+n+1)/(an*an+1),求数列{bn}的前99项和](/uploads/image/z/348576-24-6.jpg?t=%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E6%98%AF%E9%80%92%E5%A2%9E%E6%95%B0%E5%88%97%2C%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E4%B8%94a1%2Ca3%2Ca9%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2CS5%3D%28a5%29%5E2+%281%29%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F+%282%29%E8%8B%A5%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3bn%3D%28n%5E2%2Bn%2B1%29%2F%28an%2Aan%2B1%29%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8D99%E9%A1%B9%E5%92%8C)
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等差数列{an}是递增数列,前n项和为Sn,且a1,a3,a9成等比数列,S5=(a5)^2 (1)求数列{an}的通项公式 (2)若数列{bn}满足bn=(n^2+n+1)/(an*an+1),求数列{bn}的前99项和
等差数列{an}是递增数列,前n项和为Sn,且a1,a3,a9成等比数列,S5=(a5)^2
(1)求数列{an}的通项公式
(2)若数列{bn}满足bn=(n^2+n+1)/(an*an+1),求数列{bn}的前99项和
等差数列{an}是递增数列,前n项和为Sn,且a1,a3,a9成等比数列,S5=(a5)^2 (1)求数列{an}的通项公式 (2)若数列{bn}满足bn=(n^2+n+1)/(an*an+1),求数列{bn}的前99项和
1.因为
an=a1+(n-1)*d Sn=n*a1+1/2 [n*(n-1)]*d
a3^2=a1*a9 S5=(a5)^2
所以
(1) (a1+2d)^2=a1(a1+8d)
(2) 5*a1+10d=(a1+4d)^2
a1=d=3/5 a1=d=0
又因为an递增,所以d不为0
所以
an=3/5+3/5*(n-1)=3/5*n
2.
bn=25(n^2+n+1)/(9n^2+25)
后面实在不会了.