What is the P series test?
What test is used for convergence?
The Geometric Series Test is the obvious test to use here, since this is a geometric series. The common ratio is (–1/3) and since this is between –1 and 1 the series will converge. The Alternating Series Test (the Leibniz Test) may be used as well.
For which value of P does converge?
A p-series converges for p>1 and diverges for 0.
As with geometric series, a simple rule exists for determining whether a p-series is convergent or divergent. A p-series converges when p > 1 and diverges when p < 1. Here are a few important examples of p-series that are either convergent or divergent.
The p-series rule tells you that this series converges. It can be shown that the sum converges to. But, unlike with the geometric series rule, the p-series rule only tells you whether or not a series converges, not what number it converges to.
The p-series M converges for p > 1, and diverges for ps 1. 0 O C.
Therefore, the infinite series converges when p > 1, and diverges when p is in the interval (0,1).
This test measures the distance from your eyes to where both eyes can focus without double vision. The examiner holds a small target, such as a printed card or penlight, in front of you and slowly moves it closer to you until either you have double vision or the examiner sees an eye drift outward.
If limn→∞an lim n → ∞ exists and is finite we say that the sequence is convergent. If limn→∞an lim n → ∞ doesn't exist or is infinite we say the sequence diverges.