Strategy for Testing Series
1 1. If the series is of the form , it is a p-series, which we know to np be convergent if p > 1 and divergent if p 1. 2. If the series has the form arn-1 or arn , it is a geometric series, which converges if |r| < 1 and
In my lectures, I often use the following mathematical notations, which speed up my blackboard writing. Please make sure that you understand these notations: N := the set of natural numbers = the set of positive integers (not including zero) Z := t
A Caution on the Alternating Series Test
Theorem 14 (The Alternating Series Test) of the textbook says: The series (-1)n+1 un = u1 - u2 + u3 - u4 +
n=1
converges if all of the following conditions are satisfied: 1. un > 0 for all n N. 2. un un