Question

Consider the set of numbers $\{1, 3, 3^2, 3^3, \dots, 3^{100}\}$. The ratio of the last number and the sum of the remaining numbers is closest to:

Accepted Answer

B. Last number = $3^{100}$. Sum of remaining numbers = $1 + 3 + 3^2 + \dots + 3^{99} = \frac{1(3^{100} - 1)}{3 - 1} = \frac{3^{100} - 1}{2}$. Ratio = $\frac{3^{100}}{\frac{3^{100} - 1}{2}} = \frac{2 \cdot 3^{100}}{3^{100} - 1} \approx 2$.

Geometric Progression: Sum Ratio

Explanation

Practise this under exam conditions