Nth Term Test

Equation
$$\lim_{n\rightarrow oo}a_{n} = r$$

Use
Calculate the limit stated above.Once you have derived r follow these guidlines to determine the convergence.if $$r \neq 0$$ the series will diverge.if $$r = 0$$ the test was inconclusive.

Explanation
The Nth Term Test is one of the most simple tests for convergence. If the value of $$a_n \neq 0$$ when n goes to inifinity the summation of the series will just continue to add up values, and therefore diverge. If r in the above equation equals 0 then the series MAY be convergent, however another test must be used to confirm this.

Video Explanation


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