14. Use the Alternating Series Test to determine whether the series below converges or diverges. (-1)"+1 n n2 + 5 n=1

Q: Determine the convergence or divergence of the series.

A: We have to find out            ∑n=0∞(1.075)n convergent or divergent

Q: Find the radius of convergence and interval of convergence of the series. (x – 6)" 72 nš +1 n=0

A: we have to find R and I

Q: 3. Find out whether the series given below converges or diverges 1 Σ 4Vn + n=1

A: Series.

Q: Does the series from 1 to infinity of (2^k*k!)/((k+2)!) converge or diverge?

A:

Q: Find the radius and interval of convergence of the series. (л — 2)" 6" In n n=2

A: Given series

Q: 5. Show, by the alternating series test, that the series converges: >(-1)"-1 sin n=1

A: 5. The given series ∑n=1∞(-1)n-1sin1n

Q: Use the Alternating Series Test to show that the alternating series converges. 8 (-1)(e" –1) n+1 n=1

A: ∑n=1∞ -1n+1e1n-1 Suppose that for an, there exists an N so that for all n≥N 1.  an is positive and…

Q: 2. Determine whether the series converges or diverges and if the series converges, find its sum. E…

A:

Q: Find (with justification) the interval and radius of convergence of the power series: > Σ (n+1) n=2

A: We have to find

Q: 3. Decide whether or not the following numerical series converge. 5k + 4k2 (a) Σ 5k4 + In(k) + 2k +1…

A:

Q: 1 Use the comparison test to determine whether the series converges or diverges. (3n + 1)15 n=1

A:

Q: Determine whether the alternating series converges. k + 1 2(- 1)k+1. 2k + 1 k=1

A:

Q: (4-x)". /n 00 n+5 9n : 7" n=1

A:

Q: 6. Use the Ratio Test to determine if the series converges or diverges. n¹⁰2n n! n=1

A:

Q: Does the series from 1 to infinity of (3^n*n^2)/(n!) converge or diverge?

A:

Q: 17. Use the Root test to determine whether the series converges or diverges 2n=1 - 5 4n + 3\n

A:

Q: . Determine the radius and interval of convergence of the power series E(-1)*+1 n3n

A:

Q: 11) Use the Ratio Test to determine whether the series converges or diverges. (-4)2n n2 n=1 IM:

A:

Q: У7-"(10т — 1)" —п n=0

A:

Q: 9. Use the alternating series test to determine whether >(-1)"ne -n e converges or diverges. n=1

A:

Q: 3" – 1 Use the simple comparison test to determine whether the series converges 4n +n n=1 or…

A:

Q: 3 +∞ √√√n4 - 2 4n³ + 5 n=2

A:

Q: Determine whether the series converges. 1 k + 2 k=1

A: The given series,       ∑k=1∞1k+2

Q: 13) Find the radius and interval of convergence of the power series (-2)" (x+3)" 3

A:

Q: Determine the radius of convergence of the series (3n)! (n!)3 ³

A: We have to find the radius of convergence using ratio test.

Q: Determine the convergence or divergence of the series

A: The given series is ∑n=1∞4n+13n-1

Q: η3+n2 (5) Σ=o (n+1)!

A: Series ∑n=0∞ n3+n2n+1!

Q: 12. Find the interval and radius of convergence of the series k=1

A:

Q: Determine if the series converges.

A:

Q: Find the radius of convergence and interval of convergence of the (power) series. 5(2r-1)" 5"In n=1

A:

Q: 10. Determine the interval and radius of convergence for the power series. 2k (x + 2)k k=1

A:

Q: Determine whether the alternating series converges. 7ln k k k=3

A: This is a problem of series calculation. By using several test method we can decide whether series…

Q: 3. Use an appropriate method of your choice to determine whether the given series converges. Clearly…

A:

Q: Find the radius of convergence and interval of convergence of the power series. 00 x" 11. У 2n | n=1

A:

Q: Determine whether the alternating series converges. Σ k + 1 7k + 1 k=1

A: ∑k=1∞(-1)k+1k+17k+1  Above Series is an alternating seriesApply Liebnitz Testlet   ak=k+17k+1…

Q: 3 Show that the series E: is convergent and find its sum. (n+3)(n+4) n-1

A: Simplify the general term of the given series.…

Q: The series from n=1 to infinity of (16^n/2 ) / (2^2n), does this series converge or diverge.

A:

Q: 00 Calculate the radius of convergence of the power series > n5"x" n=0

A: If r=limn→∞an+1an is less than one then its convergent and if r is greater than 1 then its…

Q: 3. Determine the interval and the radius of convergence of the power series 4n+12n n+4

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: 2" (г — 8)т Find the interval of convergence of the power series m

A:

Q: 11.) Use the Ratio Test to determine the convergence or divergence of the series (n!)? (3n)! n=0

A:

Q: 2. Show that the series is conditionally convergent: n 2(-1)"-1, n2 1 n=2 For what values of p does…

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Q: 21. Find the sum of the convergent series. n =0

A: ∑n=0∞434n We can simplify, = ∑n=0∞22.2-2n3n = ∑n=0∞22-2n3n =4∑n=0∞2-2n3n  = 4∑n=0∞34n

Q: Does the series from 1 to infinity of ((3n)/(1+8n))^n converhe or diverge?

A:

Q: 8. Use the Direct Comparison Test to determine whether the series converges or diverges. a. b. n=1…

A: To use the direct comparison test to check the convergence of the given series. Direct Comparison…

Q: d) (i) Use the alternating series test to show that the series converges. k+1 k +3 Σ-) k(k+1) k=1

A: To show that the given series converges using alternating test.

Q: 12. Find the radius and interval of convergence of the power series ∞ n=1 (x-4)" √√3n

A:

Q: Find the radius of convergence and interval of convergence of the series (x + 2)" n4n n=1

A:

Q: 00 Determine the radius of convergence of the power series > (x – 2)". n=0 = i

A: Use the ratio test to find the radius of convergence of the power series ∑n=0∞(x-2)n Ratio test:…