Question: Let {xn} be a sequence and define a sequence {yn} by y 2^k := x k^2 and y 2k1 := x k for all k

Let {xn} be a sequence and define a sequence {yn} by y_2^k := x_k^2 and y_2k1 := x_k for all k N. Prove that {xn} converges if and only if {yn} converges. Furthermore, prove that if they converge, then lim xn = lim yn.

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