2. Show that the series is conditionally convergent: n 2(-1)"-1, n2 1 n=2 For what values of p does the series converge? nº 2 + n3 n=1 3.

Q: Justify the convergence of the general term numerical series: (- 1)" n? +1' n²+ 1 Where n is a…

A: consider nth term:

Q: Determine whether or not the series converges

A:

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

A:

Q: 2. Show that the series is conditionally convergent: n (-1)"-1 n² – 1 n=2

A:

Q: 3. Apply the root test to determine whether or not the series converges conditionally, converges…

A:

Q: Show that the series below is convergent. nn (2п)! n=1

A:

Q: 2. Determine if the series converges absolutely, c a. E-1(-1)" (-1)7-1 c. E=1(-1)" n+2

A: These series are alternating series test  So for convergence first we apply this test  In which if…

Q: Find the positive values of p for which the series converges.

A:

Q: Q\ Choose an appropriated series to compare with the series In(n) n3/2 n=1 and to guarantee it is…

A: Given series is ∑n=1∞un where  un=lognn32=lognnn Let us consider a series ∑n=1∞vn where vn=1n. Now,…

Q: 30. Suppose that E-o Cnx" converges when x when x = 6. What can be said about the convergence or…

A: We have the given series is ∑n=0∞cnxn is convergent for x=-4 and divergent when x=6. Let R be the…

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: Find the radius of convergence and interval of convergence of the series. E(-1)" (3n)! n=0

A:

Q: a. Investigate the convergence of the given series (2n + 1)! n²(n + 1)!" n=1

A:

Q: +0 (2х — 1)" n V4n + 1 n=0

A:

Q: Determine the convergence or divergence of the series

A: To find the series is convergence or divergence.

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

A:

Q: 3. Use the integral test to show whether the series converges or diverges 00 п a) E- 00 1 b) E: n=4…

A: Integral test:  Suppose f(x) be a continuous, positive and decreasing function on the interval [m,…

Q: Find the smallest value of x for which the series Σ (x+101)" 2ln(n) n=2 is conditionally convergent.

A:

Q: Find the interval and the radius of convergence for the series n=1 n2"

A:

Q: Find the radius and interval of convergence of the series. X=∞ and n=0 n!/2n + 1*x^n

A: Radius of converges is 0 And interval of converges is {0}

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

A:

Q: Find the interval of convergence for the series E- nx" in=D

A:

Q: Consider the series Σ (-1)" n! n=0 Show that this series converges.

A: Given series

Q: (-1)" (In n)" 4. Does the series converge absolutely, converge conditionally or diverge? n=2

A: Here, the series is an alternating series. At first we will test for the convergence and then we…

Q: Decide whether or not the following numerical series converge. 5k + 4k2 a) 5k4 + In(k) + 2k +1° k=0

A:

Q: 1. E(n + -3 2 n=1

A:

Q: 2. Verify that the infinite series converges 00 п a) E (:)" 6 n=0 00 n b) Σ-0. 6" n=0

A:

Q: E(-1)" 5n n n=1

A:

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

A:

Q: In n 32. n=1 nº ( is defined bu

A: Given ∑n=1∞ln nnp

Q: 23. Choose the series that converges: 2" b) Σ (n+1)! Θ ΣΙ2--] 3 Ο Σ 2 n-1 n=1 n-0 1 d) ο Σ n e) n=1…

A: a) Here, we find first few partial sum ,since lim sn as n approaches infinity does not exist.…

Q: Σ n" n! n=1

A:

Q: Determine whether the given series converges or diverges: 00 S(2n)! (n!)2 n=1

A: The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the…

Q: Find the values of x for which the series converges.

A: Given series - ∑n=0∞ 3x-4n Expanding the series -  putting n=0,1,2,3....∑n=0∞ 3x-4n  =…

Q: 3 +∞ √√√n4 - 2 4n³ + 5 n=2

A:

Q: (n + 2)! nn n=1

A:

Q: Determine the values of x that causing the following series to converge. (3x- 1)n 2n n=1

A: This is a problem related to convergance of the series. Based on the general formula we will answer…

Q: Determine whether the series converges or diverges. In(k) k k = 1 converges diverges

A:

Q: 18. Use the Ratio test to determine if the series converges or 2n+1 diverges En=1 n 3n-1

A: See the details solution in below

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: Does the series from 1 to infinity of (5^k)/(3^k+4^k) converge or diverge?

A: We will apply the ratio test. The test of convergence: The series will converge if the ratio of the…

Q: 3. Suppose that the following alternating series converges. (-1)" n2" Determine the number values…

A:

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

A:

Q: Determine whether the series converges or diverges. 12n2 - 8 4 n + 7 n = 1

A: Given: un=12n2-8n4+7 To prove that the given series is convergent or divergent Limit Convergent…

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: 00 2) 3) n3+5n²-17 n en n n=1 n =2

A:

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

A: