Abstract:If a continued fraction K ∞ n=1 a n /b n is known to converge but its limit is not easy to determine, it may be easier to use an extension of K ∞ n=1 a n /b n to find the limit. By an extension of K ∞ n=1 a n /b n we mean a continued fraction K ∞ n=1 c n /d n whose odd or even part is K ∞ n=1 a n /b n . One can then possibly find the limit in one of three ways: (i) Prove the extension converges and find its limit; (ii) Prove the extension converges and find the limit of the other contraction (for example, the … Show more
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