📝 Properties Of Sums

📖 From Calculus • 6. Integration • 22 questions available

Practice MCQs for Properties Of Sums. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What is the sum of the first \(n\) positive integers?

🔹 A. \(\frac{n(n - 1)}{2}\)

🔹 B. \(\frac{n(n + 1)}{2}\)

🔹 C. \(n^2\)

🔹 D. \(\frac{(n + 1)(n + 2)}{2}\)

💡 Difficulty: easy | ✅ Correct: B

Q2. A dragster travels with velocity \(v(t) = 3t^2\) meters per second over \(0 \le t \le 4\) seconds. Using a Riemann sum with 4 equal subintervals, which expression approximates the distance traveled?

🔹 A. \(\sum_{i=1}^{4} 3(i \cdot 1)^2 \cdot 1\)

🔹 B. \(\sum_{i=1}^{4} 3(i \cdot 0.5)^2 \cdot 0.5\)

🔹 C. \(\sum_{i=1}^{4} 3(i \cdot 2)^2 \cdot 2\)

🔹 D. \(\sum_{i=1}^{4} 3(i \cdot 0.25)^2 \cdot 0.25\)

💡 Difficulty: medium | ✅ Correct: C

Q3. Find a closed form for \(\sum_{k=0}^{n} \binom{n}{k} k\). Which expression is correct?

🔹 A. \(n \cdot 2^{n-1}\)

🔹 B. \(2^n\)

🔹 C. \(n \cdot 2^n\)

🔹 D. \((n + 1) \cdot 2^{n-1}\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

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