Find the value of the following expression and round to the nearest integer:
sum, from, n, equals, 1, to, 24, of, 600, left parenthesis, 1, point, 2, 6, right parenthesis, to the power n
n=1
∑
24
​	
 600(1.26) 
n
 


The given expression is a geometric series with the following general form:

\[
S = \sum_{n=1}^{24} 600 \times (1.26)^n
\]

This can be written as:

\[
S = 600 \times \left( (1.26)^1 + (1.26)^2 + \cdots + (1.26)^{24} \right)
\]

The formula for the sum \( S \) of a geometric series is:

\[
S = a \times \frac{r^n - 1}{r - 1}
\]

Where:
- \( a \) is the first term (600 × 1.26),
- \( r \) is the common ratio (1.26),
- \( n \) is the number of terms (24).

Let’s compute this geometric sum.The value of the given expression, rounded to the nearest integer, is \( 742,582 \).

Would you like further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. What is the general formula for the sum of a geometric series?
2. How does the common ratio \( r \) affect the sum of a geometric series?
3. Can you calculate the sum of the first 10 terms of a similar geometric series?
4. What happens to the sum if the common ratio is less than 1?
5. How can this method be applied to finance, such as compound interest?

**Tip**: For geometric series, if the common ratio \( r > 1 \), the terms grow rapidly, leading to a larger sum.

Find the value of the following expression and round to the nearest integer: sum, from, n, equals, 1, to, 24, of, 600, left parenthesis, 1, point, 2, 6, right parenthesis, to the power n

Learn how to calculate the sum of a geometric series with a common ratio of 1.26 and 24 terms. The series starts at 600 × (1.26)^n, and the result is rounded to the nearest integer, 742,582. This problem covers essential algebraic concepts and exponential growth, suitable for Grades 9-12.

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