Continued Fractions

a x^{2} + b x + c = 0

a_{n + 1} = \frac{3 (1 + a_{n})}{3 + a_{n}}

Fibonacci Continued Fraction
AIRA's Almost Isosceles Right Angled Triangles

n = \frac{1}{1 - n + \frac{2}{2 - n + \frac{3}{3 - n + ...}}}

1 + 2 + ... + (n - 1) = (n + 1) + (n + 2) + ... + m

Recursive seqence {1/(an+b)}
Eulers Identity Alternating sum expressed as a cf
Trigonomentric Functions Table The continued fractions expansions.
Product and Addition of cf's Closure.
Converting Power Series to Contined Fractions Issues and problem generalization.
Convergence of Periodic cfs Algebra simplification for faster convergence.
Algebraic and Visual Representation of cfs Algebra of continued fractions and circuits.

\frac{y_{n + 1}}{y_{n}} = y_{n} - y_{n - 1}

Not a cf, but an interesting number.

\sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + ...}}}

Challenges

Find the CF expansion of $\log_{b} n$ .
Find the CF for $\int_{0}^{x} e^{- x^{2}} dx$ . Derive it.
Find the continued fraction associated with $s (n) = \frac{n (n + 1)}{2}$ .
Can cf's be used to calculate the floor and ceiling functions? Reference to page 170 of Niven and Zucherman in "An Introduction to The Theory of Numbers".