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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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: 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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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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