In the short note, six proofs for the limit of ratios of consecutive terms in Fibonacci sequence are provided, including using Weierstrass-Bolzano theorem, series method, by definition of limit, difference equation method, matrix method, algebraic method.
@article{1663, title = {Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence}, journal = {CUBO, A Mathematical Journal}, volume = {5}, year = {2003}, language = {en}, url = {http://dml.mathdoc.fr/item/1663} }
Chen, Chao-Ping; Liu, Ai-Qi; Qi, Feng. Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence. CUBO, A Mathematical Journal, Tome 5 (2003) . http://gdmltest.u-ga.fr/item/1663/