Maclaurin Series (Edexcel A-Level Further Mathematics): Flashcards

Every function can be written as an infinite-order polynomial

$c_n = \frac{f^{(n)}(0)}{n!}$

$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n$

$f(0)$

$f'(0)$

$1 + x + \frac{x^2}{2}$

$x - \frac{x^2}{2} + \frac{x^3}{3} + \cdots$

Factor out the constant: $\ln[2(1 + \frac{x}{2})] = \ln 2 + \ln(1 + \frac{x}{2})$

Write as a product of known expansions

Ignore all powers greater than 2