分组求和 an=n+1/3^n
问题描述:
分组求和 an=n+1/3^n
答
Sn=(1+2+3+……+n)+(1/3+1/3^2+1/3^3+……+1/3^n) =(1+n)n/2+(1/3)(1-1/3^n)/(1-1/3) =n(n+1)/2+(1/2)(1-1/3^n) =[n(n+1)-1/3^n+1]/2
分组求和 an=n+1/3^n
Sn=(1+2+3+……+n)+(1/3+1/3^2+1/3^3+……+1/3^n) =(1+n)n/2+(1/3)(1-1/3^n)/(1-1/3) =n(n+1)/2+(1/2)(1-1/3^n) =[n(n+1)-1/3^n+1]/2