# Regrouping in Subtraction, Grade 2 Workbook

Format: Paperback

Language: English

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Let us denote the \(n^{th}\) term of the sequence of ratios by \(x_n\), that is, Then using the recursive definition of \(F(n)\) given above, we have: Now supposing for the moment that the sequence converges to a real number \(x\) (a fact which requires proof, but we’ll leave that aside), we may observe that both \(x_n\) and \(x_{n - 1}\) have the same limit, that is, Consequently, the real number \(x\) to which the sequence of ratios converges must satisfy the following equation: This is a simple equation to solve for \(x\): it is really a quadratic equation, and its positive root is the value we are looking for: This number was known to the ancient Greeks and was called by them the golden mean.

Pages: 44

Publisher: CreateSpace Independent Publishing Platform (January 1, 2016)

ISBN: 1522840087

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