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2k-1 00 (9) The sum k-13k = A) 312 9/2 C) 2 D) 2/12

2k-1 00 (9) The sum k-13k = A) 312 9/2 C) 2 D) 2/12

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 1E
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calculus medium, please solve questionnnn 9

### Mathematics Multiple Choice Questions 1. **The series \( \sum_{k=1}^{\infty} \frac{(-1)^k}{k^4/5} \) is:** - A) Conditionally convergent - B) Absolutely convergent - C) Divergent - D) D.N.E 2. **The sequence \( \left\{ (1 - \frac{3}{n})^n \right\}_{n=1}^{\infty} \):** - A) Converges to \( e^7 \) - B) Converges to \( e^{-7} \) - C) Converges to \( -7 \) - D) Diverges 3. **\( \int_{3}^{\infty} \frac{4}{x^2 + 49} \, dx = \)** - A) \( \frac{\pi}{4} \) - B) \( \frac{\pi}{2} \) - C) \( \frac{\pi}{3} \) - D) Diverges 4. **The interval of convergence of the power series \( \sum_{k=1}^{\infty} \left(\frac{x}{3}\right)^k \) is:** - A) [0] - B) \( \left(-1, 1 \right) \) - C) \((-3, 3)\) - D) \((-\infty, \infty)\) 5. **The appropriate substitution for \( \int \frac{dx}{\sqrt{x^2 + 2x + 10}} \) is:** - A) \( x+1 = 3 \tan{\theta} \) - B) \( x = 10 \sin{\theta} \) - C) \( x-1 = 2 \tan{\theta} \) - D) \( x-1 = 3 \tan{\theta} \) 6. **\( \int \frac{x}{(x+2)^2} \, dx = \)** - A) \( \frac{3}{x+3} + \ln |x+3| + c \) - B) \( \frac{2}{x+2} + \
Transcribed Image Text:### Mathematics Multiple Choice Questions 1. **The series \( \sum_{k=1}^{\infty} \frac{(-1)^k}{k^4/5} \) is:** - A) Conditionally convergent - B) Absolutely convergent - C) Divergent - D) D.N.E 2. **The sequence \( \left\{ (1 - \frac{3}{n})^n \right\}_{n=1}^{\infty} \):** - A) Converges to \( e^7 \) - B) Converges to \( e^{-7} \) - C) Converges to \( -7 \) - D) Diverges 3. **\( \int_{3}^{\infty} \frac{4}{x^2 + 49} \, dx = \)** - A) \( \frac{\pi}{4} \) - B) \( \frac{\pi}{2} \) - C) \( \frac{\pi}{3} \) - D) Diverges 4. **The interval of convergence of the power series \( \sum_{k=1}^{\infty} \left(\frac{x}{3}\right)^k \) is:** - A) [0] - B) \( \left(-1, 1 \right) \) - C) \((-3, 3)\) - D) \((-\infty, \infty)\) 5. **The appropriate substitution for \( \int \frac{dx}{\sqrt{x^2 + 2x + 10}} \) is:** - A) \( x+1 = 3 \tan{\theta} \) - B) \( x = 10 \sin{\theta} \) - C) \( x-1 = 2 \tan{\theta} \) - D) \( x-1 = 3 \tan{\theta} \) 6. **\( \int \frac{x}{(x+2)^2} \, dx = \)** - A) \( \frac{3}{x+3} + \ln |x+3| + c \) - B) \( \frac{2}{x+2} + \
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