MATH 1132Q Lecture Notes - Lecture 11: Nostril, Ibm System P, Points Of The Compass
MATH 1132Q verified notes
11/29View all
Document Summary
Math 1132q , lecture 11 , 11. 4 -- the comparison test. Basic comparison test: let a n and b n be series such that a n and b n are eventually both positive, and a n b n . If b n converges, then a n converges (if larger series converges, smaller one will also) If b n converges, then a n converges (if smaller series diverges, larger one will also) Larger numerator = larger fraction: compare terms, what we know, compare: 1/n^3 convergent , p-series , (p = 3 > 1) 1/n^3: since larger series converges, smaller series also has to converge. 4^n+n/3^n divergent geometric series ( i r i = i 4/3 i > 1 ) has to be smaller than 1. 1/11^n convergent geometric series ( i r i = i 1/11 i < 1 ) Limit comparison test: let a n and b n be series such a n and b n are eventually both positive.
