Examples. Justify your answers briefly. (a) Is ---- ) conditionally convergent or absolutely convergent? Ex- n+ nal plain your answer!

Q: Determine whether the series * absolutely convergent, conditionally convergent, or divergenE.…

A: Given series is Absolutely convergent by using cauchy root test.

Q: dæ x-1 1

A: Solution: The objective is to find whether the given integral converges or not

Q: O (D) All these statements are true. 6. Which one of the following statements is true for the…

A: Use the definition of convergent sequence and cauchy sequence to solve this problem.

Q: Rewrite the sum 2 6 (2 + ²)² + ² (2+)² η +...+ using sigma notation. 6 η (2 + 47) ² 1 n Σ. (244) 2+…

A:

Q: Which of the following statement(s) is/are TRUE ? When a function f (x) is differentiable, Newton's…

A: (i) Statement is false.Because only differentiable of f(x) is not sufficient for convergentThis…

Q: For which of the sets below, does the property n > 53 for all x, E S ?imply that (x,) is convergent…

A: which of the following is correct ?

Q: Two of the following statements are true. Which ones? 8 If Σen (*1- x0)" converges, then en (x-xo)"…

A: Note that first and last option of your questions are same.

Q: 1-n² ? 2n²+3 What is the LUB (least upper bound) of the sequence x₂ = (Note enter answer as…

A:

Q: Suppose b and c are real numbers such that b-c> 1/2. Let {b}and {c}converge to b and N, both b c…

A: Recall definition of convergence.

Q: Which of the following nfnite senes are convergent? Select all that apply. 100 100+50+25 +... %3D 2…

A:

Q: 1 n (In(n))³ n=2

A: To find that series converges or diverges

Q: Show that if an < o0, then E In(1+an) converges if and only if an converges. n=1 n=1 n=1 Hint: show…

A:

Q: (중) k 1 + 3 The seriesE is k-1 divergent convergent to O None convergent to 3 3 convergent to

A: Just use comparison test appropriately.

Q: 7 – 12n? аn+1 Let {an} be a sequence of positive real numbers such that for all values of n.…

A:

Q: Solve the initial value problem below using the method of Laplace transforms. y" - 4y' - 12y = 0,…

A: Given equation is: y"-4y'-12y=0 ,y(0)=1,y'(0)=38 We have to find the value of y(x)

Q: السؤال 9 What are all of the values of x ,such that ) (-1) n*1 converges? 6. n=1 06.2 O x26.3 0…

A: We will first find the radius of convergence, and then using it we will try to shape the interval of…

Q: Which of the followings are true? 1.En 1 nInn (-1)" is absolutely convergent. 11. En 1 (-1) is…

A: Option (e) is correct.

Q: Let an be recursively defined by ao = 2, an+1 = (an+1) for n>0. Show that an converges, and find its…

A: Given: A sequence a0=2 , an+1=14an+1. To Show: The given sequence is convergent and also find the…

Q: Instant answer or please don't attempt Un 38: Show that if Eu2 is convergent, then 2 = is convergept

A:

Q: Cauchy sequence not converge in R.A O .may not converge in set of rational numbers Q .B O converges…

A: One of the famous result in real analysis is that, Cauchy sequences converges in a complete metric…

Q: (5) Give an example for each of the following statements, if it is not possible, explain why? (a) A…

A: Let's find.

Q: (b) Determine whether the sequence 2n! + n² 2n+2n² an converges, naming any result or rule that you…

A: We shall be using trivial inequalities to solve this problem.

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

A: We have to use GP sum Common Ratio.

Q: The senes I M8 A=1 4+2-n Converges. 11

A:

Q: Aind the converg Sntenal ace of

A:

Q: cn? Let c be a nonzero real number and a, Which one of the following 29n? – 3n +7 statements is…

A: Second option is correct.