Calc III

Sequence

An ordered and infinite list of numbers: {a_n} = {a₁, a₂, a₃, a₄, … , a_n,.. }

Arithmetic sequence: Finding a_n

This is when you add or subtract the same number each time.

Geometric sequence: Finding a_n

This is when you multiply by the same number each time.

Plan of Attack for converging vs diverging sequences

1. Use limit laws as a function of f(x).

   1. Like Limit Laws, L'Hôpital's Rule, and Intermediate Forms

2. Squeeze Theorem. ALso Check for alternation to use

LLS: Sum Rule

LLS: Difference Rule

LLS: Constant Multiple Rule

LLS: Product Rule

LLS: Quotient Rule

When b≠ 0

LLS: Power Rule

Intermediate Rule

When you see 1^∞, 0^0, ∞^0 Then ln(L)=lim g(n) * ln(f(n)) Then after do L=e^lnL