Question

3. (8 points) Test the constant series for absolute convergence, conditional convergence or divergence: (a) ?_{n=1}^? (-1)^{n-1} / (n! 3^n) ; (b) ?_{n=1}^? (3n + 1) / (8n + 5) 4. (4 points) Find the radius and the interval of convergence of the power series. For what values of x does the series converge conditionally? ?_{n=0}^? (n(x+3)^n) / 5^n

          3. (8 points) Test the constant series for absolute convergence, conditional convergence or divergence:
(a) ?_{n=1}^? (-1)^{n-1} / (n! 3^n) ; (b) ?_{n=1}^? (3n + 1) / (8n + 5)
4. (4 points) Find the radius and the interval of convergence of the power series. For what values of x does the series converge conditionally?
?_{n=0}^? (n(x+3)^n) / 5^n

3. (8 points) Test the constant series for absolute convergence, conditional convergence or divergence:
(a) ?n=1^? (-1)^n-1 / (n! 3^n) ; (b) ?n=1^? (3n + 1) / (8n + 5)
4. (4 points) Find the radius and the interval of convergence of the power series. For what values of x does the series converge conditionally?
?n=0^? (n(x+3)^n) / 5^n

Added by Jonathan O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

07/26/2023

Step 1

Testing the constant series: (a) The series 3n+1 is a divergent series because it grows without bound as n approaches infinity. Therefore, the constant series is also divergent. (b) The series nt3-8n+5 can be tested using the ratio test: lim n→∞ Show more…

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3. (8 points) Test the constant series for absolute convergence, conditional convergence, or divergence: (a) ∑_{n=1}^∞ (-1)^{n-1} / (n! 3^n) ; (b) ∑_{n=1}^∞ (3n + 1) / (8n + 5) 4. (4 points) Find the radius and the interval of convergence of the power series. For what values of x does the series converge conditionally? ∑_{n=0}^∞ (n(x+3)^n) / 5^n