数列分组求和1+(1+3)+(1+3+3²）+（1+3+3²+3³）+···+[1+3+3²_数学解答

数列分组求和
1+(1+3)+(1+3+3²）+（1+3+3²+3³）+···+[1+3+3²···+3^(n-1)]=

人气：444 ℃　时间：2020-06-20 06:57:46

解答

1+(1+3)+(1+3+3²）+（1+3+3²+3³）+···+[1+3+3²···+3^(n-1)]
=(3-1)/2+(3^2-1)/2+(3^3-1)/2+.+(3^n-1)/2
=(1/2)*[3+3^2+...+3^n]-(1/2)*n
=(1/2)*3*(3^n-1)/(3-1)-n/2
=(3/4)*(3^n-1)-n/2
=(1/4)*3^(n+1)-n/2-3/4