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)