Q\ Is the sequence (Vn + 11 – vn+1)y bounded ? nEN Neither Yes No

Q: Let (s) be a sequence of real number, we say s, is Decreasing if for each nEN Sn >Sn+1

A: Given a statement

Q: +00 The sequence{Inc is n=1 (i) Converge (ii) Diverge

A:

Q: A sequence is said to be an increasing sequence if .. Vnz1 =S .a n+1 Sn2Sn+1.b O 2n.c O n+1 .d O n+1

A: A sequence is said to be an increasing sequence if...∀n≥1 To select the correct option  Sn+1 = Sn…

Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

A: Given a statement

Q: Use the Ratio Test to prove that  ∑ (2/3) (n-1) converges. n goes thru n=3 to ∞. Write step by…

A:

Q: Q. Find the limit of next sequence using the theorem for Limits n +1 2n'+1

A: Consider the provided question, given,  n2+12n2+1 We need to find the limit of the above expression,

Q: A sequence s, is said to be bounded above if there is some number N such that.... .a Sn =N .b .C…

A: Option d is correct.

Q: how whether the following infinite sequences converge or diverge : 00 {an} = 2) {bn} = {Vn6 + 12n³ –…

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Q: A Sequence is defined by the recusire rule Cn= Cn-1 , with Ci = 5 %3D which of the falawng %3D…

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Q: 3 4 N + 1 5) Show that the sequence 7 2N + 1 is bounded and monotonic.

A:

Q: 4. For the sequences L (X1, X2, x3) = (50, 40, 10) %3D and (y1, y2. y3) = (3, 1,5) %3D 3 The max of…

A: Given:x1,x2,x3= 50,40,10and y1,y2,y3=3,1,5This means x1,=50 x2,=40 x3=10and y1,3 y2,=1…

Q: +∞ Σ n² – 3n + 2 n=3

A: The sum of the given series is 5.

Q: Vhich of the followings are false? is a decreasing sequence. 2" n 1 is not a bounded sequence. (nl)…

A: For the given statement

Q: •) TT.). Suppose that X₁, X,... is an independent sequence and Y is measurable o(Xn, Xn+, ...)for…

A: From the above details we have,

Q: Which of the followings are true? 1. is a decreasing sequence. n²–1 is not a bounded sequence. I.…

A: A sequence bn is decreasing if bn+1≤bn for positive integers values of n. A sequence an is bounded…

Q: nk - k > 2 + 1' converges. n=1 Select one: O True O False

A: We will use limit comparison test

Q: The sequence an is eventually decreasing n! Select one: O True O False

A: We need to check whether the given sequence is eventually decreasing or not

Q: > The sequence {an) is n=1 (i) Converge (ii) Diverge

A: I have proved that sequence has more than one limit points.

Q: n is bounded and monotonic for all n. n +1 6. Show that the sequence An

A: The objective is to solve the above question.

Q: n! The sequence converges to 0 (100)6n Select one: O True O False

A:

Q: Choose the letter of the correct answer. If X is bounded sequence in R then X is convergent. a. True…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

Q: 43. Let {rn}-1 be a bounded sequence and {y„}=1 be a sequence tending to 0. Pro that x„yn → 0.

A: We have given that , xn be a bounded sequence. Also , yn be sequence tending to 0. We need to prove…

Q: Find an example of a sequence with the given property. a) xn - 3 and x, # 3 for all n. - 3 and the…

A:

Q: Find the limit of the sequence ´ 4n³ – 8n² – 7 1 18 – n + n4 - n=1

A: We need to find the limit of the following sequence. So,           limn→∞ 4n3-8n2-718-n+n4=limn→∞…

Q: Use limit comparison test for sum of n=1 to ♾ of (3n^3+2)^(1/2)/(8n^2+9n+1)

A: take bn = 1/n  we know that if limn→∞anbn= finite  then by limit comparison test both series behave…

Q: (b) Give an example of divergent sequences {a,} and {b,} such that {a, + bn} converges.

A: To give an example The sequences {an} and {bn} are divergent sequence such that{an+bn} converges.

Q: Prove that ∑^infinity_(n=1) ((-1)^n/n) converges.

A: Apply Ditichlet theorem.

Q: A sequence is said to be an increasing sequence if n+1 n+1 Sn2Sn+1 c O n+1

A: I will use the definition of increasing sequence.

Q: Σ n = 1 n" converges Select one: True False

A: To find whether system converge is true or false.

Q: +0o > The sequence{In(-)} is n31 (i) Converge (ii) Diverge

A: we have to test whether the given sequence is convergent or divergent

Q: Find the z trans form of the casual sequence i Xx3 where XK = C-1). %3D

A:

Q: A sequence is said to be decreasing sequence if Vn 2 1 =DS n+1 aO .b O n+1 n+12s.cO 2n.d O n+1

A: Option (b) is correct.

Q: Consider a sequence {X,,n = 1,2, 3, ·.} such that with probability Xn = 1 with probability a.s. Show…

A: @solution::::

Q: (2n)! Σ n2n converges n = 1 Select one: True False

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Q: The largest whole number k for which 2k (ke") 52n+3 (kn² + 5) n=1 converges is .....

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Q: Suppose that f0, f1, f2, . . . is a sequence defined as follows:f0 = 5, f1 = 16,fk = 7fk−1 − 10fk−2,…

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Q: 3

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Q: The sequence (-1)n+1 In=1 converge to is (i) Converge (ii) Diverge

A: The given sequence (-1)n+1n=1∞

Q: 2. Find the limit of the sequence a1 = V2v2, as ai = V2, a2 = 2/2/2, 221 %3D a4 =

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Q: A sequence is said to be decreasing sequence if Vn 21 ....... 'n+1 .a O .b O n+ 1 n Sn+12n.c O O p…

A: We need to find condition in which a sequence is said to be decreasing. The answer to the question…

Q: whether given sequences are convergent or divergent. Show your work. 4n2 +1 In 3n (b) ат — In 5n Vn³…

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Q: converges, because lim n! 2(n+1) n! = 0. (n + 1)! 2* n+00 True False Reset Selection

A: The given statement is true. Use the ratio test to find the evaluate the nth term.…

Q: Determine whether the sequences converge or diverge 1. {ne"}n=1 2. n=1

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Q: n2 The sequence is 3 +1 = 1 Select one: a. Divergent b. Convergent 8.

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Q: Find the interval of convergence for  ∑∞ n=2 (x^n)/((n^2)(3^n))

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Q: Show that n* 3-" converges for all exponents k. n=1

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Q: 2 4 N + 1 5) Show that the sequence 2N + ... ... is bounded and monotonic.

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Q: Vn2 +1 Prove that the sequence {an}n=1 converges by following the following sequence of steps n n=1…

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Q: 2n + 5 Jse the definition of sequence convergence to prove this sequence converges: 6n 3

A: Concept:

Q: an always converges. If two positive sequences {an) and {b,) converge, then the sequence Select one:…

A: Let the given sequence an converges to a  and  bn converges to b.

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.