Multiple choice

Find the sum to 9 terms of the series $0\times3+0.33+0.333+\cdots\cdots$

  1. $\displaystyle\frac{8.10^{10}+1}{27.10^9}$
  2. $\displaystyle\frac{9.10^{10}+1}{27.10^9}$
  3. $\displaystyle\frac{9.10^9+1}{27.10^8}$
  4. $\displaystyle\frac{8.10^9+1}{27.10^8}$
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A Correct answer
Explanation

The series is 0.33 + 0.333 + ... = (1/3)(0.99 + 0.999 + ...) = (1/3)((1-0.1) + (1-0.01) + ...). Sum = (1/3)(n - sum of geometric series). For n=9, this simplifies to the given expression.

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