Review question

# When does $1 + 2/3 + (2/3)^2 + \dotsb$ first exceed $0.9999S_\infty$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R9185

## Question

Find the least number of terms of the geometric series $\begin{equation*} 1 + \frac{2}{3} + \left( \frac{2}{3} \right)^2 + \dotsb \end{equation*}$

that must be taken so that the sum of these terms exceeds $99.99\%$ of the sum to infinity of the series.