The image shows a summation (Σ) notation:

$\sum_{n=2}^{47} 40(0.96)^{n-2}$

This is a geometric series where the terms are given by $40(0.96)^{n-2}$, and the summation runs from $n = 2$ to $n = 47$.

Step-by-step breakdown:

1. General term: The general term of the series is $40(0.96)^{n-2}$.
2. Number of terms: The sum goes from $n = 2$ to $n = 47$, so there are $47 - 2 + 1 = 46$ terms in the series.
3. First term: The first term when $n = 2$ is $40(0.96)^{2-2} = 40(0.96)^0 = 40$.
4. Common ratio: The common ratio $r$ is $0.96$, since each term is multiplied by $0.96$ as $n$ increases.

This series is geometric, and the sum of a geometric series can be computed using the formula:

$S_n = a \frac{1 - r^n}{1 - r}$

Where:

• $a$ is the first term,
• $r$ is the common ratio,
• $n$ is the number of terms.

Let's compute the sum using the provided values:

• $a = 40$,
• $r = 0.96$,
• $n = 46$.

I'll calculate the sum.The sum of the geometric series is approximately $847.08$.

Would you like further details or have any questions about the calculation?

Here are five related questions that might interest you:

1. How does the formula for the sum of a geometric series change if the common ratio $r$ is greater than 1?
2. What happens if the common ratio $r$ is negative?
3. Can you compute the sum of an infinite geometric series?
4. How does changing the number of terms $n$ affect the total sum?
5. Could this series be used to model real-world problems, such as depreciation or discounting?

Tip: In a geometric series, if $|r| < 1$, the series converges as $n$ approaches infinity, and the sum can be calculated using a simpler formula for infinite series.