Continued Fraction Identities/First/Infinite
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transclude this at Properties of Limit of Infinite Continued Fractions
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Theorem
Let $\left[{a_0, a_1, a_2, \ldots}\right]$ be a simple infinite continued fraction.
Then:
- $\left[{a_1, a_2, a_3, \ldots}\right] = a_1 + \dfrac 1 {\left[{a_2, a_3, \ldots}\right]}$
Proof
use continuity
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$\blacksquare$