AP Calculus BC - Geometric Series

Determine whether the following series converges or diverges. If it converges, what does it converge to?

$\sum_{n=0}^{\infty}(2)^{-2n}$

Consider: $\sum_{n=0}^{\infty} \left (\frac{\sqrt 2}{2}\right )^n$ . Will the series converge or diverge? If converges, where does this coverge to?

Calculate the sum of a geometric series with the following values:

, $a_{1}=11$ , $r=\frac{2}{20}$ ,

rounded to the nearest integer.

Calculate the sum of a geometric series with the following values:, $a_{1}=4$ , $r=\frac{1}{3}$ . Round the answer to the nearest integer.

A worm crawls up a wall during the day and slides down slowly during the night. The first day the worm crawls one meter up the wall. The first night the worm slides down a third of a meter. The second day the worm regains one third of the lost progress and slides down one third of that distance regained on the second night. This pattern of motion continues...

Which of the following is a geometric sum representing the distance the worm has travelled after 12-hour periods of motion? (Assuming day and night are both 12 hour periods).

Consider the following summation: $1+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+...$ . Does this converge or diverge? If it converges, where does it approach?

Calculate the sum, rounded to the nearest integer, of the first 16 terms of the following geometric series:

Geometric Series

Practice Questions