Suppose that an<0 for all n, and define b,=tan-(a,-n). Then the sequence {b,}... O diverges to - O converges to 0. O converges to -t . O diverges to +oo. TC converges to -

Q: 30. а, 2 1+ %3D - n

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Q: Wi n=1 (-2)^ n! n^

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Q: Find the explicit formula of the following sequence. 8 (72, 24, 8, 3, ...} O a O b Oc - Od ƒ(n) = a₁…

A: Given sequence is 72, 24, 8, 83, ...

Q: The bounded interval of the following sequence ( where n is natural number *:) is 2 sin?(3n)

A: According to the given information it is required to find the bounded interval of the following…

Q: Let the function g be defined by g(x) = (x^6 + 2)/7. Use the Fixed-Point Theorem to show that the…

A: This question is basically based on the theorem named Banach fixed point Theorem which states that:…

Q: Suppose that the sequence {n} is such that xn 20 for all n eN and that lim(-1)"xn exists. Show that…

A: We will use Triangle inequality.

Q: 1.) Prove that the sequence An= nt n In (2+1) converges to O. That is, prove limln (^+1)=0 nyo

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Q: Write out the first five terms of the sequence with, [(1-8)] determine whether the sequence…

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Q: Converges or cliverges 2:0 Inci

A: Let's Solve,

Q: Theorem 72. (Products of two convergent sequences) Let {px} be a sequence that converges to x and…

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Q: 1) In order to use the integral test, we must verify that the sequence is decreasing (and positive…

A: We have to test series is convergent or divergent

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: 4. Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing…

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Q: The set of all rational numbers in the interval (0,1) is countable, therefore it can be arranged…

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Q: Suppose (xn) is Cauchy and (yn) is bounded and monotone. Can we say anything about whether the…

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Q: Show directly from the definition that the sequence {xn}, defined by în Cauchy sequence. = 3n+2 n+1'…

A: Definition of Cauchy sequence xn of real numbers: ∀ε&gt;0 ∃ n∈N  such that |xn-xm|&lt;ε ∀m&gt;n

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: In(n) n a. Calculate the first 10 terms of this sequence. Based on these calculations, do you think…

A: As per the question we are given a sequence as : ln(n)/n And we have to : Calculate the first 10…

Q: The series 2n +2 Diverges to-o0 Converges to 1- Converges to B Diverges to +

A: Given series is ∑n=1∞sinπ2n-sinπ2n+2 The Nth partial sum of given series is…

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.