已知数列{an}中,a1=2,an+1=an²+2an(n∈N+)(1)证明数列{log2(an+1)}是等比数列,并求数列an的通项公式(2)记数列{bn}满足bn=(an)+1/(an+1),求证bn=(an+1)-(an)/(an)(an+1),并求数列的前n项和Sn
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![已知数列{an}中,a1=2,an+1=an²+2an(n∈N+)(1)证明数列{log2(an+1)}是等比数列,并求数列an的通项公式(2)记数列{bn}满足bn=(an)+1/(an+1),求证bn=(an+1)-(an)/(an)(an+1),并求数列的前n项和Sn](/uploads/image/z/4494708-36-8.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%2Ca1%3D2%2Can%2B1%3Dan%26%23178%3B%2B2an%EF%BC%88n%E2%88%88N%2B%EF%BC%89%EF%BC%881%EF%BC%89%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%7Blog2%EF%BC%88an%2B1%EF%BC%89%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%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%AE%B0%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3bn%3D%28an%29%2B1%2F%28an%2B1%29%2C%E6%B1%82%E8%AF%81bn%3D%28an%2B1%29-%28an%29%2F%28an%29%28an%2B1%29%2C%E5%B9%B6%E6%B1%82%E6%95%B0%E5%88%97%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn)
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已知数列{an}中,a1=2,an+1=an²+2an(n∈N+)(1)证明数列{log2(an+1)}是等比数列,并求数列an的通项公式(2)记数列{bn}满足bn=(an)+1/(an+1),求证bn=(an+1)-(an)/(an)(an+1),并求数列的前n项和Sn
已知数列{an}中,a1=2,an+1=an²+2an(n∈N+)
(1)证明数列{log2(an+1)}是等比数列,并求数列an的通项公式
(2)记数列{bn}满足bn=(an)+1/(an+1),求证bn=(an+1)-(an)/(an)(an+1),并求数列的前n项和Sn
已知数列{an}中,a1=2,an+1=an²+2an(n∈N+)(1)证明数列{log2(an+1)}是等比数列,并求数列an的通项公式(2)记数列{bn}满足bn=(an)+1/(an+1),求证bn=(an+1)-(an)/(an)(an+1),并求数列的前n项和Sn
a(n+1)=an^2+2an
a(n+1)+1=(an+1)^2
log2[(a(n+1)+1]=2log2[(an)+1]
log2[(a(n+1)+1]/log2[an+1]=2
{log2[a(n+1)+1]}等比数列,公比:2,首项:1
log2[(an)+1]=2^(n-1)
an=2^[2^(n-1)]-1=4^(n-1)-1
a(n+1)=an^2+2an
bn=[(an)+1]/(an+1),(分子分母同乘an)
=>bn=[(an+1)-(an)]/(an)(an+1)=1/an-1/a(n+1)
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