Question

3. Which of the following converges ABSOLUTELY? (A) sum_{n=1}^{infty} frac{(-1)^{n+1}}{sqrt[3]{n+1}} (B) sum_{n=1}^{infty} frac{(-1)^{n+1}}{n+1} (C) sum_{n=1}^{infty} frac{(-1)^{n+1}}{ln(n+1)} (D) sum_{n=1}^{infty} frac{(-1)^{n+1}}{sqrt{n+1}} (E) sum_{n=1}^{infty} frac{(-1)^{n+1}}{(n+1)^2}

          3. Which of the following converges ABSOLUTELY?

(A) sum_{n=1}^{infty} frac{(-1)^{n+1}}{sqrt[3]{n+1}}
(B) sum_{n=1}^{infty} frac{(-1)^{n+1}}{n+1}
(C) sum_{n=1}^{infty} frac{(-1)^{n+1}}{ln(n+1)}
(D) sum_{n=1}^{infty} frac{(-1)^{n+1}}{sqrt{n+1}}
(E) sum_{n=1}^{infty} frac{(-1)^{n+1}}{(n+1)^2}

$3. Which of the following converges ABSOLUTELY? (A) sumn=1^infty frac(-1)^n+1sqrt[3]n+1 (B) sumn=1^infty frac(-1)^n+1n+1 (C) sumn=1^infty frac(-1)^n+1ln(n+1) (D) sumn=1^infty frac(-1)^n+1sqrtn+1 (E) sumn=1^infty frac(-1)^n+1(n+1)^2$

Added by Connie A.

University Calculus: Early Transcendentals

Joel Hass, Christopher Heil, Przemyslaw… 4th Edition

Chapter 9

Instant Answer

Solved by Expert Sam Stansfield

05/10/2024

Step 1

A series is said to converge absolutely if the series formed by taking the absolute value of each term also converges. (A) $ \quad \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{\sqrt[3]{n+1}} $ The series of absolute values is \( \quad \sum_{n=1}^{\infty} Show more…

Show all steps