CS 2305 Sequences and Summations

Geometric Series Summation

Summation from j =0 to n of ar^j = (ar^(n+1) - a) / (r-1)

Iteration (Recurrence Relations)

1. Forward Substitution - find successive terms beginning with the initial condition and ending with a_n 2. begin with a_n and iterate until find in terms of a_1

Recurrence Relations

Defines each term of a sequence as a function of the previous term(s)

solving a recurrence relation

Finding an explicit formula for a recursively defined sequence the initial conditions specify the terms that precede the first term where the relation takes effect

Geometric Progression

f(x) = ar^x a = initial term r = common ratio

Arithmetic Progression

f(x) = dx + a d = common difference a = initial term

Factorial Function

n! = (n) * (n-1) * (n-2) * ... * (1)