设等比数列{an}的公比为q,前项和为sn,求数列{sn}的前n项和un_数学解答

设等比数列{an}的公比为q,前项和为sn,求数列{sn}的前n项和un

人气：348 ℃　时间：2020-05-23 15:17:08

解答

Sn=a1*(1-q^n)/(1-q),可得a1=(1-q)*Sn/(1-q^n)且Un=S1+S2+S3+……+Sn=[(1-q)+(1-q^2)+(1-q^3)+……+(1-q^n)]*a1/(1-q)=(n-q-q^2-q^3-……-q^n)*a1/(1-q)=[n-q*(1-q^n)/(1-q)]*a1/(1-q)=[n*(1-q)-q*(1-q^n)]*Sn/[(1-q...