Maclaurin Series 1 (AQA A-Level Further Maths): Flashcards

Function as infinite sum of powers of $x$

$f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + ...$

$-1 < x < 1$

All $x$

$-1 < x \leq 1$

Odd powers only

Even powers only

$f(0)$

$1 + nx + \frac{n(n-1)}{2!}x^2 + ...$

Expand each part separately, then multiply series together