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. This article will show how you can apply the nth term test on a given series or sequence.

2. nth Term Test （n项判断） 第n项判断 只能判别发散，不能判别收敛

2020年1月22日 · In this lecture we’ll explore the first of the 9 infinite series tests – The Nth Term Test, which is also called the Divergence Test. This test, according to Wikipedia, is one of the easiest tests to apply; hence it is the first “test” we check when trying to determine whether a series converges or diverges.

2024年8月2日 · Use the nth Term Test for Divergence to determine if a series diverges. Use the Integral Test to determine the convergence or divergence of a series. Estimate the value of a series by finding bounds on its remainder term.

In mathematics, the nth-term test for divergence[1] is a simple test for the divergence of an infinite series: If or if the limit does not exist, then diverges. Many authors do not name this test or give it a shorter name. [2] When testing if a series converges or diverges, this test is often checked first due to its ease of use.

就目前所学的内容进行一个阶段性总结： （由于是英文教材，故采取直译+英文的形式） 第n项判别法（The nth-Term Test）看该序列满不满足： \lim_ {n \rightarrow \infty}a_n = 0 ，满足即为收敛，不满足就是发散的2…

第n項測試 （the n-th term test for divergence）是數學上測試 無窮級數 是否 發散 的一個方式 [1]。 若 或極限不存在，則 發散。 許多數學書籍的作者沒有為上述的測試方式命名 [2]

第n项判别法（The nth-Term Test） 看该序列满不满足： \lim_ {n \rightarrow \infty}a_n = 0 ,如果满足 无法说明序列是收敛的;但不满足一定可以说明是发散的 [谢谢指正]

The nth Term Test for Divergence (also called The Divergence Test) is one way to tell if a series diverges. If a series converges, the terms settle down on a finite number as they get larger …

2021年5月7日 · The nth term test is inspired by this idea, and we can use it to show that a series is diverging. Ironically, even though the nth term test is one of the convergence tests that we learn when we study sequences and series, it can only test for …