数列{an}的前n项和记为Sn,a₁=2,a(n+1)=Sn+n.(1)求数列{an}的通项公式(2)求等差数列{bn}的各项为正,其前n项和为Tn,且T3=9,又a₁+b₁,a₂+b₂,a₃+b₃成等比数列.①求数列{bn
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![数列{an}的前n项和记为Sn,a₁=2,a(n+1)=Sn+n.(1)求数列{an}的通项公式(2)求等差数列{bn}的各项为正,其前n项和为Tn,且T3=9,又a₁+b₁,a₂+b₂,a₃+b₃成等比数列.①求数列{bn](/uploads/image/z/5454915-51-5.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E8%AE%B0%E4%B8%BASn%2Ca%26%238321%3B%3D2%2Ca%EF%BC%88n%2B1%EF%BC%89%3DSn%2Bn.%EF%BC%881%EF%BC%89%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%EF%BC%882%EF%BC%89%E6%B1%82%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%90%84%E9%A1%B9%E4%B8%BA%E6%AD%A3%2C%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn%2C%E4%B8%94T3%3D9%2C%E5%8F%88a%26%238321%3B%2Bb%26%238321%3B%2Ca%26%238322%3B%2Bb%26%238322%3B%2Ca%26%238323%3B%2Bb%26%238323%3B%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97.%E2%91%A0%E6%B1%82%E6%95%B0%E5%88%97%7Bbn)
数列{an}的前n项和记为Sn,a₁=2,a(n+1)=Sn+n.(1)求数列{an}的通项公式(2)求等差数列{bn}的各项为正,其前n项和为Tn,且T3=9,又a₁+b₁,a₂+b₂,a₃+b₃成等比数列.①求数列{bn
数列{an}的前n项和记为Sn,a₁=2,a(n+1)=Sn+n.(1)求数列{an}的通项公式
(2)求等差数列{bn}的各项为正,其前n项和为Tn,且T3=9,又a₁+b₁,a₂+b₂,a₃+b₃成等比数列.①求数列{bn}的通项公式;②求证:当n≥2时,1/b²₂+1/b²₂+.+1/b²n
数列{an}的前n项和记为Sn,a₁=2,a(n+1)=Sn+n.(1)求数列{an}的通项公式(2)求等差数列{bn}的各项为正,其前n项和为Tn,且T3=9,又a₁+b₁,a₂+b₂,a₃+b₃成等比数列.①求数列{bn
1、数学归纳法证明an=2^n-1,当n>=2时.
2、设bn的首项为b,公差为d>0,则由题意得3b+3d=9,(3+b+d)^2=(2+b)(7+b+2d),打开括号并将3b=9-3d代入得d^2+5d-14=0,于是d=2(d=-7舍掉).于是bn=2n-1.
3、1/1^2+1/3^2+1/5^2+...+1/(2n-1)^2