等比数列An的首项伟a,公比为q,Sn伟前n项和,求S=S1+S2+...+Sn
人气:422 ℃ 时间:2020-05-23 03:38:42
解答
等比数列前n项和的公式:Sn=a1(1-q^n)/(1-q) =(a1-an×q)/(1-q),其实就套公式S很容易可以求得,S=a1(1-q^1)/(1-q)+a1(1-q^2)/(1-q)+a1(1-q^3)/(1-q)……+a1(1-q^(n-1))/(1-q)+a1(1-q^n)/(1-q);提取同类项得:S=a1/(1-q)[(1-q^1)+(1-q^2)+(1-q^3)+……+(1-q^(n-1))+(1-q^n)]=[n-(q^1+q^2+q^3+……+q^(n-1)+q^n)]=n-q(1-q^n)/(1-q)
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