[(2/3)+(2/3)^2+(2/3)^3+……(2/3)^n]+[(1/2)+(1/2)^2+(1/2)^3+……(1/2)^n]
=[2/3-(2/3)^(n+1)]/(1-2/3)+[1/2-(1/2)^(n+1)]/(1-1/2)
当n趋向于正无穷时,（2/3)^(n+1)与（1/2)^(n+1)均为零,
所以此数列极限
lim[(4+3)/6+(4^2+3^2)/6^2+……（4^n+3^n）/6^n]
=lim[(2/3)/(1-2/3)+(1/2)/(1-1/2)]
=lim(2+1)
=3
罗嗦了一点,题目主要是要你求 两个等比数列的和