求1+(2/3)+(2/3)二次方+(2/3)三次方+……+(2/3)n次方的值

求1+(2/3)+(2/3)二次方+(2/3)三次方+……+(2/3)n次方的值

S=1+(2/3)+(2/3)二次方+(2/3)三次方+……+(2/3)n次方(1)
2/3S=(2/3)+(2/3)二次方+(2/3)三次方+……+(2/3)n次方+(2/3)n+1次方(2)
1/3S=S-2/3S=(1)-(2)=1-(2/3)n+1次方
所以:S=3-2(n+1次方)/3(n次方)