The two convergent subsequences of the sequence (-1)™+2 is a) x, = (-1)" +2 and x, = +2 %3D 2n+1 6n b) X2, =(-1)" +2 and x,1 =(-1)' +2 3n 2n+1 c) x, = (-1)" +2 and x,1 = (-1)** +2 3n d) x, =(-1)"+2 and x,-1 =(-1)" +2 %3D

Q: What is the correct answer to guess a formula for tn as a summation written in expanded form, and…

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Q: Determine if the sequence bn =  (2n2)/ln(n+5) is convergent or divergent. If converges, find the…

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Q: Consider the sequence ( 6n² + n° 3n2 – 2 Show from first principles that this sequence converges.…

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Q: QI Prove directly from the definition that the following sequence converges. (-1)" +n+1 (CoN(n*) +…

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Q: 2. Show that if a > 0, then the sequence (²x²e¬n) converges uniformly on the interval [a, ∞), but…

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Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

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Q: 3 and Xn %3D 4-Xn-1 converges. %3D Prove that the sequence defined by x|

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Q: Find all numbers x such that the series n=1 converges!

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Q: A sequence is defined by tn = tn-1 +2", and t1 = 1. Determine the fourth term in this sequence.

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Q: 2. Determine whether the series Σ (n + 1) (n + 2) converces or diverges. If converges find the sum.

A: Given series is ∑n=0∞2n+1n+2

Q: 1+2n Determine whether the series 25n 3 converges or diverges. Show all your work. n=4 Maximum…

A: Series is convergent..

Q: If the series un is convergent, n=1 then the series (−1)ª un is also convergent. n=1

A: Given first statement is true and second statement is false.

Q: Σ 3 Vn'+6

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Q: Find the Generating function for the sequence 1,3,9,27,81,. Also find for which value the series…

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Q: Find the sum of the convergent series.

A: We have to find the sum of the convergent series: 8+6+92+278+................. up to infinite. So it…

Q: 3) Justify whether the sequence converges diverges or a-an. 2-n こうe abicai b- an =(-1)"

A: Given: a. an=n2e-n, b. an=-1nn2+1n2+3

Q: ) Find the interval of conver gence of the power Series * (4)" (n-2)_ (x -2)^ | n 2" n=3

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Q: A sequence is defined by tn = tn-1+2", and t1 = 1. Determine the fourth term in this sequence.

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Q: Determine whether the sequence converges or diverges if it converges find the limit. 1. 3 + 5n а, —…

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Q: 2 a. Prove that if a, is a convergent series of nonnegative terms, then a, converges. 2 b. If we…

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Q: 3n The two convergent subsequences of the sequence (-1)+2 is

A: xn=(-1)3n+2 x2n=(-1)3(2n)+2=(-1)6n+2x2n-1=((-1)3)2n-1+2=(-1)2n-1+2    as (-1)3=-1

Q: 11. b) Determine whether the sequence an = 2- cos(n) is convergent or divergent.

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Q: Determine whether the sequence {2n+3 / 5n−7} converges or diverges.

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Q: Show that the series n" n' is convergent. Deduce that lim (2n)! (2n)! n=1

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Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: Prove that the sequence defined by a1 = −3 and an+1 = (1/4)(2an-1) converges. Then prove that it…

A: Given sequence is defined by a1=-3, and an+1=142an-1  ,n>1 We have to prove the sequence…

Q: A sequence is defined by tn=tn−1+3n and t1=1 Determine the fourth term in this sequence

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Q: Show that the series n' (2n)! is convergent. Deduce that lim (2n)! n=1

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Q: 3- (4z-5)" 5"

A: Given: ∑n=0∞4x-5n5n

Q: Determine whether the sequence converges or diverges 1+(-1)" а. An n2 b. an =(1 -3zn) 3n.

A: For the solution of the problem follow the next steps.

Q: 1. Prove that the sequence converges to . 2n+1

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Q: Prove that the sequence defined by a1 = −3 and an+1 = 14 (2an-1) converges. Then prove that it…

A: Given a sequence with recursive formula,  a1=-3, an+1=142an-1 To prove that the sequence converges.…

Q: First, find a formula for the nth term of the sequence of partial sums {Sn}. Then determine whether…

A: Given series is ∑k=1∞2k+43-2k+53ak=2k+43-2k+53 nth term of the sequence of partial sums is…

Q: Determine whether the sequence converges 1) а, 3D п sin

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Q: 2. Р, 3D 3 n21 is linearly convergent to the limit p. Generate the two terms of the sequence using…

A: Given,        pn=epn-1312,     n≥1      and     p0=0.75

Q: 9. Use the definition of convergence to prove that the sequence converges. b) {2n/(3n + 2)} c)…

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Q: : Find the interval of convergence of the power series : (8x – 8)" Σ 23n n=0

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Q: Find the interval of convergence of the series n! OA. (-00, 00) Ов. (-1,1) Oc. [-1, 1] D. [-2, 2]

A: Given a series. We need to find the interval of convergence. Let's start.

Q: the sequence converges or diverges. {an} = {: 5n5 + 8n³ – 12 } %3D n3 +3n2 -7n + 8

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Q: If Ea,x" converges on the interval [- 10,10], where does the series a, (2x - 2)" converge?

A: The Series converges on [-4,6].

Q: (a) Find the total length of the intervals removed from [0, 1] after three iterations, i.e. the…

A: (A) given interval in the starting I0=0,1 then removed the interval 13,23 that is, length removed at…

Q: 5. Determine if the series 00 3 (-1)"-1, 6n-1 n=1 Converges or diverges. Find the sum if it…

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Q: Supply a proof for Theorem 2.6.2.(Every convergent sequence is a Cauchy sequence.)

A: Solution: Consider the given statement is "Every convergent sequence is a Cauchy sequence" Let xn be…

Q: Determine whether the sequence 5n is convergent 3n2 + 2n +1

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Q: Determine if this sequence converges og diverges: n3/(cos n+ 5n)

A: We have to solve given problem: Concept:

Q: {Vn - Vn +1}

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Q: Find the first fve terms of the sequence whose general term is defined in each item. Then, give its…

A: Explanation of the answer is as follows

Q: Prove that the sequence {sin(nn/3)} does not converge.

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Q: Find the sum of the convergent series. 2 9n2 + 3n – 2 - n = 1

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Q: (a) Find the total length of the intervals removed from [0, 1] after three iterations, i.e. the…

A: This is a problem of Cantor set.

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.