📝 Summation Formulas

📖 From Calculus • 6. Integration • 19 questions available

Practice MCQs for Summation Formulas. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

Easy Questions

Medium Questions

Hard Questions

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

🔹 A. \(\frac{n(n + 1)}{2}\)

🔹 B. \(n^2\)

🔹 C. \(\frac{n + 1}{2}\)

🔹 D. \(2n\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A polygon with \(n\) sides inscribed in a unit circle has area \(A(n) = \frac{1}{2} n \sin(2\pi/n)\). What is \(A(6)\)?

🔹 A. \(\frac{3\sqrt{3}}{2}\)

🔹 B. \(\pi\)

🔹 C. \(2.598\)

🔹 D. \(3.0\)

💡 Difficulty: medium | ✅ Correct: A

Q3. Which of the following series represents the area of a circle of radius \(r\) using a power‑series expansion?

🔹 A. \(\pi r^2 = \sum_{k=0}^{\infty} (-1)^k \frac{r^{2k+2}}{(2k + 2)!}\)

🔹 B. \(\pi r^2 = \sum_{k=0}^{\infty} (-1)^k \frac{r^{2k}}{(2k)!}\)

🔹 C. \(\pi r^2 = \sum_{k=0}^{\infty} \frac{r^{2k+2}}{k + 1}\)

🔹 D. \(\pi r^2 = \sum_{k=1}^{\infty} (-1)^{k+1} \frac{r^{2k}}{k!}\)

💡 Difficulty: hard | ✅ Correct: B

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