Maclaurin Series 2 (AQA A-Level Further Maths): Flashcards

Infinite series summing to a finite value

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

All real values of $x$

$-1 < x < 1$ (for $n \in \mathbb{R}$)

$\ln(0) = -\infty$, not finite

$x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots$

Only multiply terms up to required power of $x$

$\frac{0}{0}$ or $\frac{\infty}{\infty}$

$\lim \frac{f(x)}{g(x)} = \lim \frac{f'(x)}{g'(x)}$

$\frac{(2x)^r}{r!}$ or $\frac{2^r x^r}{r!}$