How to Know Which Test to Use for Series Convergence
How to know which convergence tests to apply for a series Given P an if you are asked to compute the value of the series if it converges here are some hints. The interval of convergence of a power series is the set of all x-values for which the power series converges. Pin On Math Videos Well find the first few terms of the series using n1 n 1 n2 n 2 n3 n 3 and n4 n 4. . We must do further checks. If a series is a p -series with terms 1 n p we know it converges if p 1 and diverges otherwise. If the limit of a series is 0 that does not necessarily mean that the series converges. Geometric series are series of the form where. If you see that the terms a n do not go to zero you know the series diverges by the Divergence Test. 1 2 1 n n n. With the geometric series if r is between -1 and 1 then the series converges to 1 1 r. Deciding which convergence test to apply to a given series is often the hardest part of...