Question

find the sum of the following infinite geometric sequence. round to 4 decimal places.

\\ \left\\{4, 1, \frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \dots\
ight\\} \\

Explanation:

Step 1: Identify the first term and common ratio

$$a = 4, \quad r = \frac{1}{4}$$

Step 2: Apply the infinite geometric sum formula

$$S = \frac{a}{1 - r} = \frac{4}{1 - \frac{1}{4}}$$

Step 3: Simplify the expression

$$S = \frac{4}{\frac{3}{4}} = \frac{16}{3}$$

Step 4: Convert to a decimal rounded to four places

$$S \approx 5.3333$$

Answer:

5.3333