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] Log in to Reply

Answer:## (9n+10)^(-n)-1)/27

Step-by-step explanation:hope it helps

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]