Pascal's triangle (coefficients of $(a + b)^n$)

n=0:            1
n=1:          1   1
n=2:        1   2   1
n=3:      1   3   3   1
n=4:    1   4   6   4   1
n=5:  1   5  10  10   5   1

Each number is the sum of the two above it.

Expansion

$$(a + b)^n = a^n + \binom{n}{1}a^{n-1}b + \binom{n}{2}a^{n-2}b^2 + \dots + b^n$$ $$\binom{n}{r} = \frac{n!}{r!\,(n - r)!}$$

• The number of terms is $n + 1$.
• General term: $T_{r+1} = \binom{n}{r}a^{n-r}b^r$.
• $(1 + x)^n \approx 1 + nx + \dfrac{n(n-1)}{2}x^2 + \dots$ (use for approximations with small $x$).