Question

\( 0.2 + 0.22 + 0.022 + \cdots \) up to \( n \) terms is equal to

• A. \( \frac{2}{9} - \frac{2}{81}(1-10^{-n}) \)
• B. \( \frac{2}{9}\left[n - \frac{1}{9}(1-10^{-n})\right] \)
• C. \( \frac{2}{9}(1-10^{-n}) \)
• D. \( \frac{n}{9}(1-10^{-n}) \)

Hint:

For decimal series, convert into fractions and identify a pattern that allows splitting into geometric progressions.

Answer 1

The Correct Option is B