求数列{An}的通项公式
正数数列{An}的前项和为Sn,且2根号Sn=An+1. 试求数列{An}的通项公式. 要过程
2根号Sn =an+1 4Sn=(an+1)^ 4S(n+1) =[a(n+1)+1]^ 4a(n+1) =[a(n+1)]^-(an)^+2a(n+1)-2an ====>[a(n+1)]^-(an)^-2a(n+1)-2an=0 [a(n+1)+an][a(n+1)-an -2]=0 因为是正数数列 a(n+1)+an >0 ===> 只有 a(n+1)-an -2 =0 a(n+1) =an+2 又 2根号S1 =a1+1 ===>a1=1 ===>an =1+(n-1)*2 =2n -1
答:解: a1=S1=2a1-3,得a1=3 Sn=2an-3n S(n-1)=2a(n-1)-3(n-1) Sn-S(n-1)=2an-2a(n-1)-3=an ...详情>>
答:详情>>