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Direct linkFalcon, Sergio – International Journal of Mathematical Education in Science and Technology, 2004
It is reasonably well known that the ratios of consecutive terms of a Fibonacci series converge to the golden ratio. This note presents a simple, complete proof of an interesting generalization of this result to a whole family of 'precious metal ratios'.
Descriptors: Generalization, Inferences, Mathematical Concepts, Equations (Mathematics)
Osler, Thomas J. – International Journal of Mathematical Education in Science & Technology, 2006
Euler gave a simple method for showing that [zeta](2)=1/1[superscript 2] + 1/2[superscript 2] + 1/3[superscript 2] + ... = [pi][superscript 2]/6. He generalized his method so as to find [zeta](4), [zeta](6), [zeta](8),.... His computations became increasingly more complex as the arguments increased. In this note we show a different generalization…
Descriptors: Mathematics Education, Mathematical Concepts, College Mathematics, Computation
