We consider the sequence of real numbers (Un) defined on N by Uo = -1, U1 = 1/2 and for every n E N, U(n+2) = U(n+1) - 1/4 Un. Where N reprents the set of natural numbers. Vn = U(n+1) - (1/2)Un. We define the sequence (Wn) by for every n E N, (Wn) = Un / Vn. (i) Calculate Wo and show that Wn is an arithmetic sequence and precise its common difference. (ii) Express Wn in terms of n and calculate its limit.

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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.