a) Suppose (an) is Cauchy and that for every k∈N, the interval (−1/k,1/k) contains atleast one term of (an). Can we say that (an) converges to 0? Either show that it does or give a counter-example. b) Suppose (xn) is Cauchy and (yn) is bounded and monotone. Can we say anything aboutwhether the sequence (xn yn) converges or not? Justify your answer!

Q: 3. Suppose {fa) is an equicontinuous sequence of functions on a compact set K, and U.) converges…

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Q: 2. Consider the following bounded and increasing sequence: a₁ = √3 a2 V √3+√√3 a3 = √√3+√3+√3 √√3+…

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Q: 1. Prove that the sequence converges to . 2n+1

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Q: 6. Consider the sequence defined recursively by 1 2 an+1 = an + N an If ao = 1, does the sequence…

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Q: converges

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Q: True or False: The generating function of the sequence h₁=n+1 is 1/(1-x)². O True False

A:

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.