2. Determine if the given sequence converges or diverges. If it converges, what is its limit? (e) an = In(6n* – 4) – In(3n² + 5n² – 7n + 8) (f) {cos(nx)}o

Q: 1. Define when a sequence X = (x,) in R is said to converge to x E R. Then prove that the sequence X…

A: The given sequence is: xn=3n+12n+5

Q: Calculate the limit of the sequence an = Cos( 10πη3 – 3. 5n³+ n²

A:

Q: 2. n=2 nlogn does not converge but En-2 nlog²n converges. Show that Z2 [Hint: you might find it…

A:

Q: 5. Determine if Σn=3 convergent. cos(NT) is absolutely convergent or conditionally n+1

A: "Absolute convergence" means a series will converge even when you take the absolute value of each…

Q: 1. Write out the first eight terms of each of the following sequences: (b) {(-1)"} (a) { // } (c)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub￾parts for…

Q: 3. Assume the sequence of positive numbers (sn) increases monotonically to infinity. Prove that Sn+1…

A: Let Sn be a sequence of positive numbers sn increase monotonically to infinity. ⇒limn→∞sn=∞     ∵ sn…

Q: 2. an = 3 +- + cos(2nz) п 3. an = In(14n – n) – In(3n° + 2n² + 1) - |

A:

Q: 1. The sequence (x,) is defined by the following formulas for the nth term. Write the first five…

A: We have to write the first five terms of the given sequence.Note: According to the guidelines we are…

Q: 1. Determine whether the following sequences converge or diverge. If the sequence diverges, state…

A:

Q: Define the sequence{xn}by (see photo). Prove, using the epsilon −N definition, that this sequence…

A:

Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

A:

Q: 3. Let for n € N. Is convergent? a₁ = 1, an+1 Σ n=1 = An sin an

A:

Q: Σ(-1). , where [.] denotes the greatest integer function, is [cos n] (n + 1)² n=1 O absolutely…

A: Solution:-

Q: 7. The famous Rodrigues formula states that H, (x) = (-1)"e*² (4)" functions for positive integers…

A:

Q: Find the limit of this sequence. 1 Vn sin Vn An

A:

Q: 1 Ei=1 limn→00 n+i 2]

A:

Q: Let r > 0 be a positive real number. This problem will give a simple approach to limn→∞ rn. i.…

A:

Q: 5ln(n) In(3n) converges or diverges, if it converges, find its limit. 1.- Determine if the sequence…

A:

Q: Determine if the given is convergent or divergent. (x²+1)² n Zn=1 (n²+1)²

A:

Q: (iv) COS x -dx, 3.

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

Q: 1/16 Perform a test to determine if tan (80)d0 converges. b lim tan(80)d0 b-x/ 16" 0 (Simplify your…

A:

Q: 10 Suppose we want to obtain a root of x-x-10 = 0. We can rewrite it as x = If we use the 8-1 10…

A:

Q: [ 1+2x)e*dx is convergent

A:

Q: {fn(x)}1 converges a.e. to a function f(x) to be determined.

A:

Q: Find the sequence for the generating functionG (x) = (1-x) 1-x

A:

Q: Determine the sequence of the generating function A(8) = – log. (1 – s)\s |

A:

Q: Suppose G(r) is the generating function of a sequence (an), satisfying G'(r)=rG(r), G(0) = 1. iii.…

A:

Q: Q(A). Let {fn(x)}-1 00 n%=D1 be a sequence of functions (1+ (x – 2)* S, - defined over [2,3]. Show…

A:

Q: QUESTION 1. Consider the sequence (x,)EN, Where x,=1 and x,=v2 + x,1. Show that (a) (x)nEN is…

A: When the value of x is increasing with respect to the increased value of y.It is monotonically…

Q: Show Recurrence that the solution to T (n) = T (2n/3) + 1 is Θ( log2 n)

A:

Q: Suppose G(r) is the generating function of a sequence (an)o, satisfying G'(r) =rG(r), G(0) = 1. i.…

A: Solution : G'(r)=r G(r) G'(0)=0×G(0)=0 ∫G'(r)G(r)=∫r G(r)=cer22 G(0)=1c=1 G(r)=er22 G(r)=∑i=0∞x2ii!

Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

A:

Q: Write out the first five terms of the sequence, determine whether the sequence converges, and if so…

A: Given,      an = n2 + 3n - na1 = 1,   a2 = 10 -2,    a3  = 18 -3,   a4 = 28 -4,  a5  = 40 -5by…