Question

If \( \Delta r = \left| \sum_{r=1}^{n} r \right| \), then \( \sum_{r=1}^{n} \Delta r \) is equal to

• A. \( \sum_{r=1}^{n} r^2 \)
• B. \( \sum_{r=1}^{n} r \)
• C. \( \sum_{r=1}^{n} r^3 \)
• D. \( \sum_{r=1}^{n} r^4 \)

Hint:

The sum of the first \( n \) integers is given by the formula \( \frac{n(n+1)}{2} \).

Answer 1

The Correct Option is B

The sum of \( \Delta r \) is the sum of integers from 1 to \( n \), which is simply the sum \( \sum_{r=1}^{n} r \).