9514 1404 393
Answer:
(9n +10^(-n) -1)/27
Step-by-step explanation:
The tricky part is figuring out how to describe the series. The general term can be described by ...
an = (1/3)(1 -10^(-n))
Then the sum of n terms is ...
[tex]\displaystyle\sum_{k=1}^n{\frac{1-10^{-k}}{3}}=\frac{n}{3}-\frac{1-10^{-n}}{30(1-10^{-1})}=\boxed{\frac{9n+10^{-n}-1}{27}}[/tex]
