PreCalc- Sigma K formulas and Summation Formulas

Arithmetic- nth term

f(n) = f(1) + d(n-1)

Arithmetic- Sum of first n terms

s(n) = n/2 * (f(1)+f(n))

Geometric- nth term

f(n) = f(1)* r^n-1

Infinite Sum formula

s=f(1)/1-r, -1<r<1

Σc formula

Σc= nc

Σk formula

Σk = n(n+1)/2

Σk² formula

Σk² = n(n+1)(2n+1)/6

Σk³ formula

Σk³= (n(n+1)/2)²

First Step of a Mathematical Induction Proof

Base case

Second Step of a Mathematical Induction Proof

Hypothesis- assume true when n=k

Third Step of a Mathematical Induction Proof

Prove true when n=k+1

Fourth Step of a Mathematical Induction Proof

Proof substitute in hypothesis

Last Step of a Mathematical Induction Proof

Therefore statement ∴ + ∀𝗇∈𝖭

Fifth step of aMathematical Induction Proof

BOOOOM or DOOM

Geometric- Sum of first n terms

f(1)*((1-r^n)/1-r)