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: B) Prove that the sequence is convergent, where az = v2, = v2, 2+an, an+1 = %3D n 2

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Q: 1 lim n→∞ n² 0 =

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Q: 1 2n+3 - whether an C. Is the sequence bounded? is increasing, decreasing or not

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Q: (c) Prove that the sequence is Cauchy and conclude that it therefore converges.

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Q: {Vn - Vn +1}

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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.