Ratio Test

Last updated Jan 18, 2022 Edit Source

• Math analysis
• Math calculus

Let $\sum a_n$ be a series such that $a_n \neq 0$. Then, calculating the limit

$$ \lim_{n\to\infty} \frac{|a_{n+1}|}{|a_n|} = L $$

We have three cases:

• If $L < 1$, the series converges
• If $L > 1$ the series diverges
• If $L = 0$ or the limit is non-existent, then the test is inconclusive