Home > Calculus > Nth Term Test for Divergence of an Infinite Series

How do you use the Nth term test on the infinite series #sum_(n=1)^oosin(n)# ?

Answer 1

Elijah Abram

Since #lim_{n to infty}|sin(n)|# does not exist, #lim_{n to infty}|sin(n)| ne 0#

By Nth Term Test (Divergence Test), we can conclude that #sum_{n=1}^infty sin(n)# diverges.

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Answer 2

William Abdalla

To use the Nth term test on the infinite series ( \sum_{n=1}^{\infty} \sin(n) ), you evaluate the limit of the Nth term ( a_n = \sin(n) ) as ( n ) approaches infinity. If the limit is not zero, then the series diverges. If the limit is zero, the test is inconclusive, and you may need to use other convergence tests to determine the convergence or divergence of the series.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.