1+1/3+1/(3^2)+1/(3^3)+……+1/(3^n)=?
问题描述：
1+1/3+1/(3^2)+1/(3^3)+……+1/(3^n)=?
答
Sn=1+1/3+……+1/(3^n),3Sn=3+1+1/3+……+1/[3^(n-1)],3Sn-Sn=2Sn=3+1-1+1/3-1/3+……+1/[3^(n-1)]-1/[3(n-1)]-1/(3^n)=3-1/(3^n),即Sn=3/2-1/[2*3^n]