1. Using ratio test determine whether the series converges absolutely or diverges n2(n + 2)! >(-1)3n. n! 32n n=1

Q: 3. Determine whether the series is convergent or divergent. State reasons. n3 (a) L 2n³ – 1 +1 n=1

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Determine whether the series converges. k Σ In(k + 3) k=1 O The series diverges. O The series…

A:

Q: 3. Find the radius of convergence and interval of convergence of the series (3x + 2)" (a) n! n=1

A:

Q: 8. Determine whether the series is conditionally convergent, absolutely convergent, or divergent: 1…

A: Explanation of the solution is given below..

Q: Determine whether the series converges. k In(k + 2) The series converges. O The series diverges.

A: The given series is ∑k=1∞kln(k+2)

Q: Determine if the series converge absolutely, converges, or diverge 5n2 + 9 E (-1)n n=1 |8n8 +6…

A: The given series is: ∑n=1∞(-1)n5n2+98n8+6 Let, an=(-1)n5n2+98n8+6|an|=5n2+98n8+6

Q: b) Use the Ratio Test to determine if the series converges diverges. or n5" (2n + 3)ln (n + 1) n=1

A:

Q: # 1) Determine if these series converge or diverge (don't guess). If they converge, find their sum.…

A:

Q: Determine the convergence or divergence of the series. (If you need to use co or -co, enter INFINITY…

A: The given series is ∑n=1∞-1n8n-13n+1. The given series converges if the limit limn→∞8n-13n+1 exists.

Q: 3. Determine whether or not the series converges. Justify your conclusion. 86 Σ n=1 n² - 2n n³ + 3n+…

A: Solution is given below:

Q: Use the Ratio Test to determine if the series converges or diverges. 0* 4"n² n=1 n! a. The limit of…

A: Given : ∑n=1∞ 4nn2n!To check whether the given serie is convergent or divergentLet an=4nn2n! ;…

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: 16. Determine if the alternating series converges or diverges E-1(-1)n+1. Make sure to check that 2n…

A:

Q: Determine the convergence or divergence of the series

A:

Q: 37. Find the radius of convergence of the infinite series o(2" + (-1)"3")(x – 4)".

A:

Q: 1 Σ n%3D1 n

A: The given series is ∑n=1∞1n-1n2n To find: Find convergence or divergence of the series.

Q: 10. Find the interval of convergence and the radius of convergence of the power series (x-4)" n·9"…

A:

Q: 1 Prove that the series converges n(ln n)3 n=2

A:

Q: V. Consider the power series +∞o Σ n=1 (x + 1)n 3√√n² + 1 1. Determine whether the resulting series…

A: Use Leibnitz test(given in next page) to show convergence at x=-4.For 2) use radius of convergence…

Q: Determine whether the series converges. k 2 In(k + 3) k=1 O The series diverges. O The series…

A:

Q: Determine the convergence or divergence of the series. (If you need to use co or -0o, enter INFINITY…

A: Explanation of the answer is as follows

Q: Use the Ratio Test to determine the convergence or divergence of the series. 4n2 5" n = 1 n + 1 lim…

A:

Q: n°(x – 2)" 3n n=1

A:

Q: (b) Determine whether the series n=1 n 3n+2 n is convergent or divergent.

A: See this solution in below

Q: (-1)* Use the Ratio Test to determine the convergence or divergence of the series 2 n=1 converges

A:

Q: Test the convergence or divergence of the series by Root Test k k k Ek=1 Lk=1 5k E-1(1 – e-k)k 100

A:

Q: 8. Find the radius of convergence and interval of convergence of the series Eo (а-2)" n2+1 n=0

A:

Q: Determine whether the series converges. 1 k=1 1) To determine whether a given series converges, it…

A:

Q: Determine convergence or divergence of 18+(-1)" n=D1 using any method covered so far. The series…

A:

Q: 5. Determine whether the series converges absolutely or conditionally or diverges. y (-1)" a. Ens2 n…

A:

Q: Please need solution for number 4

A:

Q: Test the convergence or divergence of the series by Root Test k Ek=1 5k E-1(1 – e-k)k Ek=1 100,

A: solution: the given series are∑k=1∞k100k,∑k=1∞k5k,∑k=1∞1-e-kkTo test convergence on divergence of…

Q: 1. Find the radius of convergence and interval of convergence of the series. (a) (-1)"(n+1)"a²" n=1

A:

Q: k! (2k + 1)! k=1

A:

Q: Determine the convergence or divergence of the series

A: The given series is ∑n=1∞4n+13n-1

Q: Determine whether the alternating series converges. k + 1 >(- 1)k+1 6k + 1 k=1 O The series…

A:

Q: Determine whether the series converges or diverges. There may be more than one correct way to…

A:

Q: 2. Determine whether or not the series converges. State clearly the test you use, and show all…

A: We have to check the convergence

Q: Use the Ratio Test to determine the convergence or divergence of the series. 2n n = 1 an + 1 lim an…

A:

Q: 1 Determine whether the series > Σ diverges. converges or k (k + 7) (k + 4)

A: Given that,                ∑ f(x)=∑ 1k(k+7)(k+4)for checking convergence and divergence first we…

Q: 11) Find the radius and interval of convergence of (x + 3)" Σ the series n = 1 n!

A:

Q: Q2: Test the series converges or diverges by integral test -2n n=1

A: we have to determine whether the given series is convergent or divergent by using integral test

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

A:

Q: Test the convergence or divergence of the series by Absolutely Alternating Test E(-1)*2 ΣR=3(-1)k…

A: A aeries of the form is called an alternating series. The convergence of such series can be found…

Q: 8) Determine whether the series (- 1)" Σ n = 1 7n - 1 is absolutely convergent, conditionally…

A: Follow the steps.

Q: Determine whether the series converges. k Σ In(k + 3) k=1 The series converges. O The series…

A:

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

A:

Q: 3. Find all values of x such that the series > (x – 6)" is convergent. n=1

A:

Q: Determine the convergence or divergence of the series

A: Known fact: If limn→∞ an ≠0  then ∑n=1∞ an diverges.

Q: 14. Use the Alternating Series Test to determine whether the series below converges or diverges.…

A: