Sure! To find the sum of this series, let's first identify the pattern. Each term in the series is half of the previous term:
\[ 1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \dots \]
This is a geometric series with the first term (\(a\)) equal to 1 and the common ratio (\(r\)) equal to \( \frac{1}{2} \).
The formula to find the sum (\(S\)) of an infinite geometric series is:
\[ S = \frac{a}{1 - r} \]
Substitute the values into the formula:
\[ S = \frac{1}{1 - \frac{1}{2}} \]
\[ S = \frac{1}{\frac{1}{2}} \]
\[ S = 2 \]
So, the sum of the series is 2.
Hope this helps!
