AP: a_n=a+(n-1)d, S_n=n(2a+(n-1)d)/2=n(a+l)/2 GP: a_n=ar^(n-1), S_n=a(r^n-1)/(r-1), S_inf=a/(1-r) for |r|<1 HP: Reciprocals in AP; HM=2ab/(a+b)

Means: AM=(a+b)/2, GM=sqrt(ab), HM=2ab/(a+b) Inequality: AM>=GM>=HM; AM*HM=GM^2

Standard Sums:

• sum(k)=n(n+1)/2
• sum(k^2)=n(n+1)(2n+1)/6
• sum(k^3)=[n(n+1)/2]^2
• sum(2k-1)=n^2
• sum k(k+1)=n(n+1)(n+2)/3

Telescoping: 1/(k(k+1))=1/k-1/(k+1); sum=n/(n+1) AGP infinite: S=a/(1-r)+dr/(1-r)^2

Conditions:

• AP: 2b=a+c
• GP: b^2=ac
• HP: b=2ac/(a+c)

Insertion:

• k AMs between a,b: d=(b-a)/(k+1), sum=k(a+b)/2
• k GMs between a,b: r=(b/a)^(1/(k+1)), product=(ab)^(k/2)

From S_n: a_n=S_n-S_(n-1) for n>=2; if S_n=An^2+Bn then d=2A