Pure Mathematics 2

$u_n = a + (n - 1)d$

$S_n = \tfrac{n}{2}\left[2a + (n - 1)d\right]$

$u_n = ar^{n-1}, \quad S_n = \dfrac{a(1 - r^n)}{1 - r}$

$S_\infty = \dfrac{a}{1 - r}$

$(a + b)^n = \sum_{r=0}^{n} \binom{n}{r} a^{n-r} b^r$

$\log_a x = y \iff a^y = x$

$\log a + \log b = \log ab, \quad \log a^n = n\log a$

$\sin^2\theta + \cos^2\theta = 1$

$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$

$\int_a^b y\,dx \approx \tfrac{h}{2}\left[y_0 + y_n + 2(y_1 + \dots + y_{n-1})\right]$