Question
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Answer
The sum of 5 from \( t=6 \) to \( t=40 \) is 175.
Solution
To evaluate the sum:
\[
\sum_{t=6}^{40} 5
\]
This notation means that we are adding the number 5 for each integer value of \( t \) from 6 to 40, inclusive. Here's how to compute it step by step:
1. **Determine the Number of Terms:**
The number of terms in the sum can be found by subtracting the lower limit from the upper limit and then adding 1 (since both endpoints are inclusive).
\[
\text{Number of terms} = 40 - 6 + 1 = 35
\]
2. **Multiply by the Constant Value:**
Since each term in the sum is 5, you multiply the number of terms by 5.
\[
\text{Sum} = 35 \times 5 = 175
\]
**Final Answer:**
\[
\sum_{t=6}^{40} 5 = 175
\]
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Simplify this solution Bonus Knowledge
To evaluate \( \sum_{t=6}^{40} 5 \), we can notice that the expression is asking for the sum of the constant \( 5 \) from \( t = 6 \) to \( t = 40 \). The number of terms in this summation is \( 40 - 6 + 1 = 35 \). Since each term contributes \( 5 \), we multiply \( 5 \) by the total number of terms: \[ 5 \times 35 = 175. \] So, \( \sum_{t=6}^{40} 5 = 175 \).
