Question

Let {an} and {bn} be two Cauchy sequences of real numbers. Prove or give a counter example for the

following statements.

(a) There exists α ∈ (0, 1) such that |an+1 − an| < α|an − an−1| for all n ≥ 2.

(b) The sequence {a

2

n

bn} is a Cauchy sequence.

(c) The sequence {|an − bn|} is a Cauchy sequenc​

Answer 1

Answer:

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