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Cauchy's first Theorem on limit16. If be a sequence of real n... | Filo

Cauchy's first Theorem on limit16. If be a sequence of real n... | Filo

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SOLVED: Q. (3). (a): Prove that the product of two Cauchy sequences is again a Cauchy sequence. Is the converse true? Explain. (3 2-5) (b): What is the main difference between finitely oscillating sequences and infinitely oscillating sequences? Give an example of any four infinitely oscillating sequences. (c): Give an example of a convergent sequence of irrational numbers. Let lim(n->0) 0, then prove that lim(n->0) (1/1 1/2 ... 1/n) = 0.

SOLVED: Q. (3). (a): Prove that the product of two Cauchy sequences is again a Cauchy sequence. Is the converse true? Explain. (3 2-5) (b): What is the main difference between finitely oscillating sequences and infinitely oscillating sequences? Give an example of any four infinitely oscillating sequences. (c): Give an example of a convergent sequence of irrational numbers. Let lim(n->0) 0, then prove that lim(n->0) (1/1 1/2 ... 1/n) = 0.

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