Question
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum is \( 5 \times (41 - b) \).
Solution
To evaluate the summation:
\[
\sum_{t=b}^{40} 5
\]
This represents adding the constant value 5 for each integer value of \( t \) starting from \( t = b \) up to \( t = 40 \).
### Step-by-Step Evaluation:
1. **Identify the Number of Terms:**
The number of integer values from \( t = b \) to \( t = 40 \) is:
\[
\text{Number of terms} = 40 - b + 1 = 41 - b
\]
(We add 1 because both endpoints \( b \) and \( 40 \) are included.)
2. **Calculate the Sum:**
Since each term in the summation is 5, the total sum is:
\[
\text{Sum} = 5 \times (\text{Number of terms}) = 5 \times (41 - b)
\]
3. **Final Expression:**
\[
\sum_{t=b}^{40} 5 = 5(41 - b)
\]
### Example:
If \( b = 30 \), then:
\[
\sum_{t=30}^{40} 5 = 5(41 - 30) = 5 \times 11 = 55
\]
### Conclusion:
The evaluated sum is:
\[
\sum_{t=b}^{40} 5 = 5(41 - b)
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To evaluate the sum \( \sum_{t=b}^{40} 5 \), you first notice that since the term being summed is a constant (5), this makes things simpler. The sum counts the number of terms from \( t = b \) to \( t = 40 \). The number of integers from \( b \) to \( 40 \) is \( 40 - b + 1 = 41 - b \). Thus, you can compute the total sum as \( 5 \times (41 - b) \). So, the final expression is: \[ 5 \times (41 - b) = 205 - 5b \]
