数列0.7,0.77,0.777,0.7777...7(n个7),求an,S10.

a_n=7/9*(1-1/10^n).
S_{10}=7.6913580247.
S_{10}
=7/9*sum_{n=1}^{10}(1-1/10^n)
=7/9*(10-sum_{n=1}^{10}10^{-n})
=7/9*(10-0.1(1-10^{-10})/0.9)
=7.6913580247.

an=7*【10^（-1)+10^(-2）+。。。。。。+10……（-n）】
=7*10^(-1)*(1-0.1^n)/(1-0.1）
=7/9*(1-0.1^n)
s10=7/9*[(1-0.1^1)+(1-0.1^2)+......+(1-0.1^10)
=7/9*{10-0.1*(1-0.1^10)/(1-0.1)}
=7/9*{10-0.1111111111}
=7/9*9.8888888889
=7*1.0987654321
=9.6913580247