MATH 1ZB3 Study Guide - Midterm Guide: Stochastic Process, Exponential Sum
11 Dec 2013
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Summary notes for 1zb3 midterm 1 (part one) Rearrange everything (should probably look at lecture 4 if not sure how: conclusion: works for every point of the list. If it comes to a number, it converges (or looks like it"s going to go to a number) Dne, or infinity means it diverges (looks like it"s doing random shit like rising or not moving, or flopping between positive and negative) Telescoping sums: type of sum (bn+bn+1, compute sm (same as in a series), most terms will cancel with the telescoping property, evaluate the limit directly. Recurrence relation defined sequences: when a term is defined by a function of the preceding term, an+1=1/4(an+a) , a1=1, bounded + monotonic = convergent, can use induction to show bounded & monotonic, bounded: an has a restricted range. Ex: an is between 0 and 100: monotonic: stays consistently in the same direction. Ex: 1, 2, 3, 4, 5 : anything else is divergent.
