3. Let 2n2 + 3 |an| < for alln E N. n3 + 5n2 + 3n +1 Show (using definition of Cauchy Sequence) that {an} is a Cauchy sequence.

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A: (16) Given that , fx=x2-3x+2 and gx=2x3-4x+1 find f+g in Z7x.

Q: 5. The subsequence of (xn) = () is.. a) (1층..) 0) (1.층,급.) b) (1,1,1, ..) a) (1.-) 6. The sequence…

A: Every subsequence has a pattern.  According to guidelince we solve only first question.

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Q: 6. The sequence (xn) = (3,3,3,3, ...) is .. a) not Cauchy b) unbounded c) divergent d) convergent

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A: Mathematical induction: For all-natural numbers, the principle of mathematical induction is a…

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Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: 3. Define Cauchy sequence and prove that the sequence { } is a Cauchy sequence in C[1,3]. nt+5

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A: Given  be a Cauchy sequence. The equivalence class of this sequence is a real number.The aim is to…

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A: Introduction:       A grouping of numbers in a specific order is known as a sequence. On the other…

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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.

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Q: an 57" n! nal

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

Q: Prove that if {n} is a real sequence that satisfies 2n² +3 |xn| ≤ n³ +5n² + 3n+ 1 for all n E N,…

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