Rapid Revision Bullets

AP: a_n = a+(n-1)d -- use (n-1), not n
GP: a_n = ar^(n-1), S = a(r^n-1)/(r-1)
Infinite GP: S = a/(1-r), converges only if |r|<1
sum(k) = n(n+1)/2
sum(k^2) = n(n+1)(2n+1)/6
sum(k^3) = [n(n+1)/2]^2 = [sum(k)]^2
AM >= GM >= HM; equality iff all equal
AM*HM = GM^2 for two positive numbers
1/(k(k+1)) = 1/k - 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: 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