The sum of the terms of the infinite geometric series 1, 0.86, 0.86², 0.86³, ..., is closest to which of the following numbers? A)B0 B)1.86 C)7.14 D)0.54 E)116.28

Question

Quizplus · Accepted Answer

The common ratio is 0.86, and the first term is 1, so the sum can be calculated using the formula $S = \frac{a_1}{1-r}$, where $a_1$ is the first term and $r$ is the common ratio.

Plugging in, we get:

$S = \frac{1}{1-0.86} = \frac{1}{0.14} = \frac{100}{14} = \frac{50}{7} \approx 7.14$

Therefore, the sum is closest to $\boxed{	extbf{(C) }7.14}$.

The Sum of the Terms of the Infinite Geometric Series