设等比数列{an}的前n项和为Sn已知an+1=Sn+2(n属于N+)(1)求数列an的通项公式(2)若bn=1/log2an乘以log2an+1,求数列{bn}的前n项和Tn
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![设等比数列{an}的前n项和为Sn已知an+1=Sn+2(n属于N+)(1)求数列an的通项公式(2)若bn=1/log2an乘以log2an+1,求数列{bn}的前n项和Tn](/uploads/image/z/13420205-53-5.jpg?t=%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%E5%B7%B2%E7%9F%A5an%2B1%3DSn%2B2%EF%BC%88n%E5%B1%9E%E4%BA%8EN%2B%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97an%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%882%EF%BC%89%E8%8B%A5bn%3D1%2Flog2an%E4%B9%98%E4%BB%A5log2an%2B1%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn)
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设等比数列{an}的前n项和为Sn已知an+1=Sn+2(n属于N+)(1)求数列an的通项公式(2)若bn=1/log2an乘以log2an+1,求数列{bn}的前n项和Tn
设等比数列{an}的前n项和为Sn已知an+1=Sn+2(n属于N+)(1)求数列an的通项公式(2)若bn=1/log2an乘以log2an+1,求数列{bn}的前n项和Tn
设等比数列{an}的前n项和为Sn已知an+1=Sn+2(n属于N+)(1)求数列an的通项公式(2)若bn=1/log2an乘以log2an+1,求数列{bn}的前n项和Tn
(1)
a(n+1)=Sn+2
an=S(n-1)+2
两式相减得 a(n+1)-an=an
即 a(n+1)=2an
因此an为等比数列
又 a2=2a1=a1+2 故a1=2
于是 an=a1*q^(n-1)=2^n
(2)
bn=1/[log2an*log2an+1]=1/[n*(n+1)]
Tn=b1+b2+.+bn
=1/(1*2)+1/(2*3)+.+1/(n*(n+1))
=1-1/2+1/2-1/3+.+1/n-1/(n+1)
=1-1/(n+1)