(a) Is each of the following a Cauchy sequence in R? Justify your answer. 3ne n2 Vns+3n²+2 i. The real sequence {xn} defined by x, = Vn E N. %3D ii. The real sequence {yn} defined by yn = "TVn E N. n(-1)" 2n+1 : (b) Let {zn} be a real sequence defined by 1 z1 = 5, zn+1 = V5zn+12 – - for n> 1. n

Q: Find the sum of the first 6 terms of the sequence defined by an = -4 (2)^-¹ for n ≥ 1. -

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Q: Q4: Find the following sequence: Then Make sketch of -3 x(n) = 3n[u(n+3)-u(n-4)] y(n) = x(2n-3)

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A: the definition of a subsequence of a sequence Xn.

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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.