1. One of the following sequences is divergent 1 (A) an 72 (B) S, = k=1 (-1)" (C) cn = 2n3 (D) b, = (-1)". n3 +1

Q: x-1 Given p(x) = (.33)(.67)^', x = 1, 2, 3... %3D Find p(2). O A. .7789 о в. 2211 О с. 33 D. none of…

A: Let X be the random variable having probability mass function is,  P(X) = (0.33)*(0.67)x-1 ,     x =…

Q: (1) Suppose that (an) tends to infinity. (a) Suppose that (bn) tends to minus infinity. What can you…

A: Let's delve into a detailed step-by-step explanation: (a) Sequence ( (anbn) ) as ( n ) goes to…

Q: 1. Give an example of a sequence {an} where lim(an+2 – an) = 0 but {an} is divergent.

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Q: Find the fourth partial sum of the series, E8(-)", where n = 1 to 4 Show all of your steps. Enter…

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Q: How would I find if the sequences an=nπ cos(nπ) and an= (n2)(1/n) are convergent/divergent?

A: To examine the given sequence regarding convergence, that is study the limits as n tends to infinity

Q: FIND THE TAYWR FUR f (x) = 7 X4 SERIES ABOUT X=-3

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Q: Find P(16) of the sequence defined by P(1) = 1,P(2) = 2, P(n) = P| PG) + 2P ( ), ‚n > 1

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Q: Determine the sequence of the generating function A(s) = (1– 2 -9)2 |s| < 1

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Q: Given the sequence Of (n)=2+2 Of (m) = 2 + 1/ n Of(n)=n+: 1+n Of (n)=3--1/ = 21/1, 23, 2441... what…

A: The given sequence is 212, 213, 214,... The objective is to find f(n). A map from ℕ to ℝ defines a…

Q: 17. Let (Hn) be a sequence defined by Hn k' k=1 1 0, n +1 (b) Deduce that In(n + 1) < Hn < Inn+1…

A: Note: Since we can solve first three subparts of a question, we have solved the first three…

Q: The sequence shows the total number of rodents in an abandoned warehouse at the end of each month…

A: Given the sequence is 16, 24, 36, 54, 81,  …

Q: Consider the following sequences n G In (1+n) (ii) e^/ (n²+1), (iii) √√n²+ √n²+2n -n. Which of the…

A: Let {an} be a sequence of real numbers If an≤an+1 ∀ n∈N then the sequence an is called monotonically…

Q: 2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: 12. Prove the following facts about the Fibonacci sequence (Fn): (1) (Chapter 10, #26) E-1 F =…

A: Given, The Fibonacci sequence (Fn) Fn=Fn-1+Fn-2, where F0=0 &amp; F1=1

Q: Re-index each of the following sequences to start at the indicated initial index 1 no = 3 and no 12…

A: To re-index a sequence a1, a2, a3,…,an…, starting from n0=k, we change the formula by replacing n by…

Q: 2. Write the first five terms of of each recursively-defined sequence. t(1) = 3t(n + 1) =- 2-t(n)…

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Q: Determine the generating function of the following sequence {1(2), 2(3), 3(4),... } Select one: O a.…

A: The objective is to determine the generating function for the sequence

Q: 1) Write down the first 5 terms of each of the following sequences: {bn}a_1, where bn = nth digit of…

A: SOLUTION:

Q: (a) (b) Find the limit of the following sequences or show why they diverge. In(5n6) 1 7n-1 +n8 8n³ +…

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Q: an = (-1)", bn Cn = n² dn= n (a) For each sequence, give an example of a monotone subsequence. 6n +…

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Q: L{5cosh2t-3sinht} 1. 5s 3 a. s²-4 s²-1 3 5s b. s²+4 s²-1 3 5s C. s²-4 s²+1 5s 3 d. s²-4 s²-1 - +

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Q: gent subsequer O an = (-2)" O an = 1+ (-1)" · 10(-1)"-n n sin () %3D O an = O an = 1+2· (-1)"

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Q: 1- 5: Express the following as sequence of the indicated terms: 1 Ea, +- 1. 2' 10 а, 'i+1 2. 3.

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

Q: 5. Find są and the maximum error for: n=0 Use the integral test for the error. (Hint, write the…

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Q: 13. Let (an)=I be a Cauchy sequence, and let p : N → N be a one-to-one function. Show that the…

A: A sequence is called a Cauchy sequence if as the sequence progresses, the terms of the sequence…

Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence, as  an…

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Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

Q: Problem 6. Write the results of the following summations. Use the the sequences from 4(a) and 4(d)…

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Q: ne following - {un! n п — 1 n (1) ап n =n – Vn2 n 2/n (2) аn п. - (3) аn — 3".4" (4) ап — п!

A: We will evaluate the limit

Q: {dn} = SA { (. (₁₁²³²7) - (₁~^²+₁ ) ) ²^ } - (ⓇP) :)

A: The given sequence is defined by the formuladn=15((1+52)n−(1−52)n) We can find the first five terms…

Q: Q(3) The sequence 4n3 3n7 + n3 2n7 (a) Converges to (b) Diverges (c) Converges to

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Q: By redefining the ranges of the summations appearing on the left-hand side, show that En(n –…

A: Consider the left hand side Substitute n = n+2 in first summation, thus it becomes By…

Q: lim (n22n) / n! = ?

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.