求和:(a-1)+(a²-2)+…+(a∧n-n),(a≠0)
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求和:(a-1)+(a²-2)+…+(a∧n-n),(a≠0)
求和:(a-1)+(a²-2)+…+(a∧n-n),(a≠0)
求和:(a-1)+(a²-2)+…+(a∧n-n),(a≠0)
稍等
=(a+a^2+...+a^n)-(1+2+3+...+n)=(a(a^n-1))/(a-1)+n*(n+1)/2
稍等
(a-1)+(a^2-2)+......+(a^n-n)
=a+a^2+a^3+...+a^n-(1+2+3+...+n)
就是一个等差数列和一个等比数列
若a=1,那么原式=n-(1+2+...+n)=-n(n-1)/2
若a≠1,那么原式=a(1-a^n)/(1-a)-n(n+1)/2