Question

实数数列满足下列条件,对任意正整数n,该数列的前n项平方和加上n恰好等于前n项和的2倍,求该数列的通项

Answer 1

a1^2+a2^2+a3^2+a4^2+a5^2+.+an^2+n=2（a1+a2+a3+a4+a5+.+an)(a1^2-2a1+1)+(a2^2-2a2+1)+.+(an^2-2an+1)=0(a1-1)^2+(a2-1)^2+.+(an-1)^2=0故a1=1,a2=1,a3=1,.an=1,故 通项为an=1