数列｛an}的前n项和为Sn,已知a1+2,Sn+1=Sn-2nSn+1Sn,求an紧急紧急!求救中!sos_数学解答

数列｛an}的前n项和为Sn,已知a1+2,Sn+1=Sn-2nSn+1Sn,求an
紧急紧急!求救中!sos

人气：247 ℃　时间：2019-10-25 17:27:54

解答

我会我会Sn+1=Sn-2n Sn+1Sn 两边同除以Sn+1 *Sn得 1/Sn+1 - 1/Sn = 2n以此类推 1/Sn - 1/Sn-1 = 2(n-1)1/Sn-1 - 1/Sn-2 = 2(n-2)...1/S2 - 1/S1 = 2以上各个式子相加得1/Sn - 1/S1 = 2(1+2+...+n)=n(n+1)而1/S1=1/2=...