设数列an的前n项和为Sn,满足an+Sn=An^2+Bn+1（A不等于0）,a1=3/2,a2=9/4,求证an-n为等比数列并_数学解答

设数列an的前n项和为Sn,满足an+Sn=An^2+Bn+1（A不等于0）,a1=3/2,a2=9/4,求证an-n为等比数列并求an

人气：138 ℃　时间：2019-10-11 10:55:15

解答

解析：当n=1时,a1+S1=A+B+1；即A+B=2；当n=2时,a2+S2=2a2+a1=2*9/4+3/2=6=4A+2B+1,即4A+2B=5联立以上两式,可得A=1/2,B=3/2.由题意：an+Sn=An^2+Bn+1 ①则a(n+1)+S(n+1)=A(n+1)^2+B(n+1)+1 ②②-①,可得：a(n+1)-an+a...