Question

是否存在常数a,b,c使得数列{an}的首项a1=1,通项公式是an=an^2+bn+c,且对于任意的正整数n,{an}

Answer 1

假设存在!3Sn=(n+2)*An 3Sn-1=(n+1)*An-1 3An=(n+2)*An-(n+1)*An-1 (n-1)An=(n+1)An-1 An/An-1=(n+1)/(n-1) An=(An/An-1)*(An-1/An-2)*.*(A2/A1)*A1 =[(n+1)/(n-1)]*[(n)/(n-2)]*.*(3/1)*1 =n(n+1)/2 (n>1时) 又A1也...