a) Does f() -Σne" n=0 converge or diverge for r > 0? b) How do you know?

Q: tan (x) +n In(n+2) 04: Determine the convergence of , on A=[0,+).

A: given fn=∑n=1∞tan-1xx2+n2lnx+2  on A=[0,∞) claim- to determine the convergence

Q: How to prove {sin(n)} is a bounded seuqence that does not converge?

A: To prove xn=sinn is bounded. By definition, a sequence xn is bounded if it is both bounded above and…

Q: en Σ 11. nn n=1

A:

Q: Determine the convergence or divergence of serie sin Σ 6n2 n +4 n=1

A:

Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.

A:

Q: 00 Suppose that p(r) = > anc" converges on (-1, 1], find the internal of convergence of p(3x – 7).…

A: Given that ∑n=0∞anxn converges on (-1,1]  To find the interval of converges of p(3x-7)

Q: 5) The interval of convergence is: a) (-2,2] b) (-2,2) ed to show that c) (-2,2) d) [-2,2] ()…

A:

Q: Consider fr2/3 dr. Compute the experimental order of convergence when us- ing (a) the composite…

A:

Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

A:

Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

A:

Q: Find the radius of convergeune ļ interal of convergence : (a) (x-z)" n=0 (b) そ1 n.g"

A:

Q: Use the Ratio Test to determine the convergence or divergence of the s -INFINITY, respectively.)…

A:

Q: Determine whether converges absolutely, converges condi- 2" cos n n=0 tionally, or diverges.

A:

Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

A:

Q: What are all of the values of x such that (-1)"+1 Σ (3)" converges?

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

Q: Decide whether the following proposition is true or false. Provide a justification for your answer:…

A:

Q: Σ (d) n (In(n))2

A:

Q: 04: A) Discuss the convergence of f,(x) =, , on A-(0, 0).

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Σ n 1 (n+2) n=0

A: Given series is ∑n=0∞ xn+1(n+2)!

Q: 7. Use the Ratio Test to show that has radius of convergence 3" R = /3. n=0

A: To find the radius of convergence: a) find the (n+1)th term which is denoted as an+1 b) find the…

Q: (b) Give an example to show that the product (fngn) may not converge uniformly.

A:

Q: The interval of converge Use your own wo each step) that yo

A:

Q: Converge or diverge with what test?

A:

Q: Two sequences of functions fn and gn that converge uniformly but fn In does not converge uniformly.

A: See the attachment

Q: A. converges B. diverges

A: Given that the series: A. ∑n=1∞15n B. ∑n=1∞n+6n2+12n+4 To find check the series converges or…

Q: Use the Ratio Test to prove convergence or divergence: 2n+2 (n+2! (n+2). n=1

A:

Q: 3. Show that the ratio test is inconclusive, but use either the integral or a comparison test to…

A: Given the series:

Q: (-1)" In(n) Vn n=2

A:

Q: What are all of the values of x, such that converges?

A: We have to use GP sum Common Ratio.

Q: prove convergence or divergeence A) is similar to E by using the Limit Comparison Test tan B)…

A:

Q: 3- a- By definition show that (x,) = (+3) converges to 3. b- Does (+3) bounded, Cauchy? Show by part…

A:

Q: tan (x) n' In(n+2) 04: Determine the convergence of A=[0,+). on

A: Let the sum of the series be given by Sn. ⇒Sn=∑n=0∞tan-1(x)x2+n2ln (n+2) un=∑ n=0∞tan-1(x)x2+n2ln…

Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: Suppose that p(æ) > anx" converges on (-1, 1], find the internal of convergence of p(6x – 9). n=0

A:

Q: 27 n! n=0 converges to 0. 8.

A:

Q: What does the nth-Term Test for Divergence say about the following scrics? use the Integral Test to…

A: if integral is finite then series is convergent

Q: Converge or diverge with what test?

A:

Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

A:

Q: E 2 ( – 13" An(n)/2" | .......

A:

Q: 2n+1 4. Use the definition to prove that ) converges.

A:

Q: Use the ratio test to find the radius of convergence for En (z - 3)". n=0

A:

Q: Q No 2: a) Discuss the convergence and divergence of (1+ a"), Va eR.

A: We have to divide it into several cases.

Q: fn (x) = Vx e (1, 00), Vn E N. Explain why the sequence {fn} does not satisfy the conclusion of the…

A:

Q: 1.4 Does (fa(r)} in 1.3 converges uniformly on |-3,3]? Explain.

A:

Q: 04: A) Discuss the convergence of f,(x)=x+- -.on A [0,0).

A:

Q: (e) $₁ = 5 and Sn+1 = √√4s +1 for n ≥ 1.

A: Given s1 = 5 and sn+1 = 4sn+1 for n≥1