Question
Question Find the numerical answer to the summation given below. \[ \sum_{n=0}^{100}(7 n+2) \] Answer Attempt 1 out of 3
Ask by Wells Burns. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The numerical answer is 35552.
Solution
Calculate or simplify the expression \( \sum_{n=0}^{100}(7n+2) \).
Find the sum by following steps:
- step0: Solution:
\(\sum _{n=0}^{100}\left(7n+2\right)\)
- step1: Calculate:
\(\sum _{n=0}^{100}7n+\sum _{n=0}^{100}2\)
- step2: Calculate:
\(35350+\sum _{n=0}^{100}2\)
- step3: Calculate:
\(35350+202\)
- step4: Add the numbers:
\(35552\)
The numerical answer to the summation \( \sum_{n=0}^{100}(7n+2) \) is 35552.
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Simplify this solution Mind Expander
To compute the summation \( \sum_{n=0}^{100}(7n+2) \), we can break it into two separate sums: 1. The sum of \( 7n \): \[ \sum_{n=0}^{100} 7n = 7 \sum_{n=0}^{100} n = 7 \cdot \frac{100(100 + 1)}{2} = 7 \cdot 5050 = 35350 \] 2. The sum of the constant \( 2 \): \[ \sum_{n=0}^{100} 2 = 2 \cdot 101 = 202 \] Now, we add these two results together: \[ \sum_{n=0}^{100} (7n + 2) = 35350 + 202 = 35552 \] So, the numerical answer to the summation is \( 35552 \).
