Find the sum of the following infinite geometric series: \( 5+2.5+1.25+0.625+\ldots \) 8 10 7

To find the sum of the infinite geometric series \( 5 + 2.5 + 1.25 + 0.625 + \ldots \), we can use the formula for the sum of an infinite geometric series: \[ S = \frac{a}{1 - r} \] where: - \( a \) is the first term of the series. - \( r \) is the common ratio between consecutive terms. **Step 1: Identify \( a \) and \( r \)** - The first term \( a = 5 \). - The common ratio \( r \) can be found by dividing the second term by the first term: \[ r = \frac{2.5}{5} = 0.5 \] **Step 2: Apply the formula** \[ S = \frac{5}{1 - 0.5} = \frac{5}{0.5} = 10 \] **Conclusion:** The sum of the infinite geometric series is **10**. **Answer:** 10