Rapid Revision Bullets

AP: $a_n$ = a+(n-1)d -- use (n-1), not n
GP: $a_n$ = ar^(n-1), S = a $\frac{r^n-1}{(r-1)}$
Infinite GP: S = $\frac{a}{1-r}$ , converges only if |r|<1
sum(k) = n $\frac{n+1}{2}$
sum( $k^2$ ) = n(n+1) $\frac{2n+1}{6}$
sum( $k^3$ ) = [n $\frac{n+1}{2}$ ]^2 = [sum(k)]^2
AM >= GM >= HM; equality iff all equal
AM*HM = $GM^2$ for two positive numbers
$\frac{1}{k(k+1}$ ) = 1/k - $\frac{1}{k+1}$ -- telescoping
AGP: use S-rS technique
Three in AP: assume a-d, a, a+d (sum = 3a)
Three in GP: assume a/r, a, ar (product = $a^3$ )
HP: convert to AP of reciprocals, no direct sum
$S_n$ = $An^{2+Bn}$ => AP with d = 2A (no constant term!)
$a_n$ = $S_n$ - S_(n-1) for n>=2; check $a_1$ = $S_1$
k*k! = (k+1)!-k! -- telescoping identity
Rationalize: $\frac{1}{sqrt(k}$ +sqrt(k+1)) = sqrt(k+1)-sqrt(k)
x + k/x >= 2*sqrt(k) for x>0 (AM-GM)
log converts GP to AP; exponential converts AP to GP
Sum of first n odd numbers = $n^2$