Question

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

Answer 1

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

Explanation:

hope it helps

Answer 2

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Answer:

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

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{(1-10^(-k))/(3)}=(n)/(3)-(1-10^(-n))/(30(1-10^(-1)))=\boxed{(9n+10^(-n)-1)/(27)}`