数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式
问题描述：
数列an是首次为1的正数列,且(an+1)²/n - an²/n+1 + (an+1*an)/(n+1)n =0,求通项公式
数列an是首次为1的正数列,且(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,求通项公式
答
(an+1)²/n - an²/(n+1) + (an+1*an)/(n+1)n =0,(n+1)(an+1)² + (an+1*an)- nan² =0,[(n+1)a(n+1)-nan]*[a(n+1)+an]=0a(n+1)+an>0(n+1)a(n+1)-nan=0则{nan}是等差数列,公差为0,即为常数列首项为1...