MATH 1005 Study Guide - Final Guide: Ibm System P, Conditional Convergence, Absolute Convergence

• School: Carleton University
• Department: Mathematics
• Course: MATH 1005
• Professor: Zahra Montazeri

Document Summary

In most convergence tests, the given initial value of n is either 0 or 1, but the tests will work with any initial value of n. Geometric series: the geometric series diverges when |r| 1. Note: starting the series at a di erent initial value of n will not a ect convergence, but it will change the sum. Telescoping series: sometimes the term being summed can be written so that a lot of cancellation takes place in the partial sum sn, making it easy to nd s = lim sn (which is the sum of the series). See example 6. 45 in the text. n nth term test: if lim n an 6= 0, then. Note: the nth term test can not be used to show that a series converges. Integral test: let f be positive, continuous, and decreasing for x 1, and let an = f (n). Xn=1 an converges if and only if z .