已知数列｛an}满足a1=1,a2=3,若n为奇数a(n+2)=an+1若n为偶数a(n+2)=3an,求证数列｛a(2k)}为等比数列2.｛an}的通项公式3.{an}的前n项和

Question

已知数列｛an}满足a1=1,a2=3,若n为奇数a(n+2)=an +1若n为偶数a(n+2)=3an,求证数列｛a(2k)}为等比数列
2.｛an}的通项公式3.{an}的前n项和

Answer 1

1.n为偶数,A(n+2)=3An,偶数项成等比数列,A2k=3^k,An=3^(n/2)2.n为奇数,A(n+2)=An+1,奇数项成等差数列,A(2k-1)=k,An=(n+1)/2An=(n+1)/2 n为奇数An=3^(n/2) n为偶数3.n为奇数奇数项和S(2k-1)=(1+k)k/2 S奇=(n+1)(n+3)/...