Question

Sum of n terms of series 0.3, 0.33, 0.333,.......

Answer 1

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 ...

  $\displaystyle\sum_{k=1}^n{\frac{1-10^{-k}}{3}}=\frac{n}{3}-\frac{1-10^{-n}}{30(1-10^{-1})}=\boxed{\frac{9n+10^{-n}-1}{27}}$

Answer 2

Answer:

(9n+10)^(-n)-1)/27

Step-by-step explanation:

hope it helps