nth Term Test/Limit Test
Definition
The nth Term Test, also known as the Limit Test, is a method used to determine the convergence or divergence of a series. It states that if the limit of the terms in a series does not equal zero, then the series diverges.
Analogy
Imagine you have a jar filled with marbles. If you keep adding more and more marbles to the jar without ever stopping, eventually it will overflow. Similarly, if the terms in a series keep getting larger and larger without approaching zero, then the series will diverge.
Related terms
Convergence: A series is said to converge if its terms approach a finite value as more terms are added.
Divergence: A series is said to diverge if its terms do not approach a finite value as more terms are added.
Infinite Series: An infinite sum of numbers written in the form of ∑(a_n), where n ranges from 1 to infinity.
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