Find the sum of the infinite geometric series. 2 + 1 + 1/2 + 1/4 + Write your answer as an integer or a fraction in simplest form. ______

Substitute values into formula: Now that we have the first term and the common ratio, we can use the formula for the sum of an infinite geometric series: S = a_1 / (1 - r) Substitute the values of a_1 and r into the formula: S = 2 / (1 - (1/2))Perform calculation: Perform the calculation inside the parentheses first: 1 - (1/2) = 1/2 Now, substitute this value back into the formula: S = 2 / (1/2)Divide by reciprocal: To divide by a fraction, multiply by its reciprocal: S = 2 * (2/1) S = 4

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the sum of the infinite geometric series. $\newline$ $2 + 1 + \frac{1}{2} + \frac{1}{4} + \dots$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ $\_\_$

View step-by-step help

Home

Math Problems

Algebra 2

Find the value of an infinite geometric series

Full solution

Q. Find the sum of the infinite geometric series.

\newline

2 + 1 + \frac{1}{2} + \frac{1}{4} + \dots

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

\_\_

Substitute values into formula: Now that we have the first term and the common ratio, we can use the formula for the sum of an infinite geometric series: $\newline$ $S = \frac{a_1}{1 - r}$ $\newline$ Substitute the values of $a_1$ and $r$ into the formula: $\newline$ $S = \frac{2}{1 - (\frac{1}{2})}$
Perform calculation: Perform the calculation inside the parentheses first: $\newline$ $1 - \left(\frac{1}{2}\right) = \frac{1}{2}$ $\newline$ Now, substitute this value back into the formula: $\newline$ $S = \frac{2}{\left(\frac{1}{2}\right)}$
Divide by reciprocal: To divide by a fraction, multiply by its reciprocal: $\newline$ $S = 2 \times \left(\frac{2}{1}\right)$ $\newline$ $S = 4$