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Intro to Continued Fractions - √z as a Continued Fraction

As a small introduction to continued fractions, often used for finding rational approximations to irrational constants, in this video we build one for √z (principle branch) using a difference of squares factorization of z - 1 and find the range of convergence for complex inputs z (considering only real inputs goes through the same process and analysis). Lots of parallels can be drawn to infinite series. Timecodes: 0:00 - Finding the continued fraction 3:17 - Outline of convergence for continued fractions 9:08 - Determining convergence 18:18 - Special case of z = 0 Addendum: If you want negative real roots, just take the positive root and multiply by i in the formula, also you can multiply by -1 to get the other branch of the square root Sources and other tidbits: Continued Fraction: https://mathworld.wolfram.com/Continu... Generalized Continued Fraction: https://en.wikipedia.org/wiki/General... Approximations in Desmos: https://www.desmos.com/calculator/zvs... Twitter -   / michaelmaths_   Instagram -   / michaelmaths_  

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