Geometric sequence formula nth term8/16/2023 ![]() The nth term test utilizes the limit of the sequence’s sum to predict whether the sequence diverges or converges. A sequence is said to be converging when the sequence’s values settle down or approach a value as the sequence approaches infinity.A sequence is diverging when the sequence’s values do not settle down as the sequence approaches infinity.We make use of the sequence’s $n$th term to determine its nature, hence its name.īefore we dive right into the method itself, why don’t we go ahead and review what we know about diverging and converging sequences? The nth term test helps us predict whether a given sequence or series is divergent or convergent. We’ll also review our knowledge on divergence and convergence, so let’s begin by understanding the nth term test’s definition! What is the nth term test? Recall how we can find the sum of a geometric series and sequences.įor now, let’s go ahead and understand when the nth term test is most helpful and when it’s not.Refresh what you know about arithmetic series and sequences.Review your knowledge on applying the limit laws and evaluating limits.Make sure to review your knowledge on the following topics as we’ll need them in identifying whether a given series is divergent or convergent: This article will show how you can apply the nth term test on a given series or sequence. The nth term test is a technique that makes use of the series’ last term to determine whether the sequence or series is either converging or diverging. It is important for us to predict how sequences and series behave in higher mathematics and whether they converge or diverge. ![]() The nth term test is a helpful technique we can apply to predict how a sequence or a series behaves as the terms become larger. Nth Term Test – Conditions, Explanation, and Examples ![]()
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