Question

7. Which of the following series are conditionally convergent? (i) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{3 / 5}} \) (ii) \( \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{\sqrt{n^{5}+3 n^{2}+2}} \) (iii) \( \sum_{n=1}^{\infty}(-1)^{n} e^{-n} \) (a) all of them (b) (i) and (ii) only (c) (i) only (d) none of them (e) (iii) only

          7. Which of the following series are conditionally convergent?
(i) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{3 / 5}} \)
(ii) \( \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{\sqrt{n^{5}+3 n^{2}+2}} \)
(iii) \( \sum_{n=1}^{\infty}(-1)^{n} e^{-n} \)
(a) all of them
(b) (i) and (ii) only
(c) (i) only
(d) none of them
(e) (iii) only

7. Which of the following series are conditionally convergent?
(i) ∑n=1^∞((-1)^n)/(n^3 / 5)
(ii) ∑n=1^∞((-1)^n n^2)/(√(n^5+3 n^2+2))
(iii) ∑n=1^∞(-1)^n e^-n
(a) all of them
(b) (i) and (ii) only
(c) (i) only
(d) none of them
(e) (iii) only

Added by Kelly G.

University Calculus: Early Transcendentals

Joel Hass, Christopher Heil, Przemyslaw… 4th Edition

Chapter 9

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Solved by Expert Ishana K

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A series \(\sum_{n=1}^{\infty} a_n\) is conditionally convergent if it converges when its terms are taken with their signs (i.e., as they are), but it diverges if all terms are taken as positive. This typically involves alternating series where the terms decrease Show more…

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7. Which of the following series are conditionally convergent? (i) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{n^{3 / 5}} \) (ii) \( \sum_{n=1}^{\infty} \frac{(-1)^{n} n^{2}}{\sqrt{n^{5}+3 n^{2}+2}} \) (iii) \( \sum_{n=1}^{\infty}(-1)^{n} e^{-n} \) (a) all of them (b) (i) and (ii) only (c) (i) only (d) none of them (e) (iii) only