SearchOnMath

The \(k\)th Fibonacci number can be written in closed form as \(F(k) = \frac{\varphi^k - (-\frac{1}{\varphi})^k}{\sqrt{5}}\), where \(\varphi\) is the celebrated golden ratio.

The normal density, \(p(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\), has become important in many applications because of its close relationship to the central limit theorem.

The natural logarithm can be expanded into a series, yielding \(\ln(1+x) = \sum_{k=1}^{\infty} \frac{(-1)^{k+1}x^k}{k}\).