Mark all of the sequences that have a convergent subsequence. O{n}₁, where an is the digit in the nth decimal place of 1/ O {(-n)"}_1 O{n+ (-1)"}_1 O {(-1)"}_1 O {[cos(n)]}1, where [x] means the greatest integer less than or equal to

Q: Prove that the sequence {sin n + cos n is bounded. =1

A: The given sequence is We have to prove that the sequence is bounded.

Q: 8WI (-1) 3n+6 O Absolutely Convergent O Conditionally Convergent O Divergent

A: The given series .To determine the series absolutely convergent, conditionally convergent, or…

Q: (1) A sequence an is given by a₁ = √2, an+1 = √2+ an. (a) By induction or otherwise, show that an is…

A: As per the guidelines only one question with subparts can be answered at a time, please repost other…

Q: 2. Determine whether the following sequence converges, and if so, find its limit. (a) nn (b) {n°e-»}…

A:

Q: Let ao 1 and an 2an-1 + 1 for every n ≥ 1. Let G(r) be the generating function of the sequence ao,…

A: Introduction: The generating function is a power series representation of a recurrence relation.…

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: Consider the following sequence, un+1 = log2 (n +1+ un) for n EN' where u1 = 1. Show that for each n…

A:

Q: Which of the following is a bounded sequence? 0 {1} O {n sin n} °{(-1)} {(−1)²+1_ non} cos n

A:

Q: Given a sequence x₁, x2,... of real numbers, show that cos(x₁) + + cos(xn) exists if and only if…

A:

Q: - - 9. - [1.0001 x* H. Verify Let A 6 = the error %3D 1.0001 formula |r* – ô|| ||r|| < K(A)-

A: Let A=2112, b=33, x^=1.00011.0001, x*=11. Verify the error formula x*-x^x*≤KArb.

Q: n+1 1. Σ. Znal 2n- 3

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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: (a) Test the convergence or divergencc for the sequence {sinh(ln n)} and find lim sinh(ln n). n++00

A: The given sequence,        limn→+∞sinhln n

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

A: Solution:-

Q: 1. Let an = 5n 4n3 5 This sequence converges to L = 4 (a) Find the smallest N EN such that |an — L|…

A:

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

A:

Q: The integral tests says that if an=f(n), then the series 2 an is convergent if and only n =1 if the…

A: for integral test three conditions must be satisfied for the function i.e.  continuous, positive and…

Q: Which of the following sequences is convergent? Select one: O a. lim, v00 n² +1 3n /n15 n2 cos(1/n)…

A: b

Q: b) List down the first four terms in the expansion of (1 2x) -2 in ascending power of x. Hence, by…

A:

Q: Calculate the limits by arguing with the power series representations of each function. Tipp: 4 =…

A: We can expand each function into its corresponding power series and then assess the limit by looking…

Q: \° over (0, 0) is x² + n?x Q.The sequence of functions 2x + 3n²x ) n=1 a. Not convergent.…

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Find monotonicity, convergence or divergence, and bounds (if…

A: Monotonic sequence : A sequence is called Monotonic if it is either increasing or decreasing as n…

Q: For the sequence an = n cos n n² +1

A: given a sequence

Q: Find the first three terms of the sequence (B₁f) of Bernstein polynomials for f(x) = x³.

A: The sequence of Bernstein polynomials for a function f(x) is defined as follows:B_n^k(x) = C(n, k) *…

Q: 1 n > 3. Let an nInn +00 (a) Show that the sequence {an}=3 is decreasing.

A:

Q: Which of the following statements are true? Vn² sin(n²) 1. n+1 I. lim II. Let {an} be a convergent…

A:

Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: Let the sequence {fn(x)} be defined on [0, 1] by n – n2x; if x E (0, ) fn(x) : otherwise SHOW THAT:…

A: The given sequence is fnx=n-n2xif x∈0,1n0otherwise First to find the limit function of this sequence…