Math Tools

Ratio Test Calculator

by The Scientific Place

∑n=N∞\sum_{n=N}^{\infty}

The following series will be tested:

∑n=N∞(2n)!n!\sum_{n=N}^{\infty} \frac{\left ( 2 n \right ) !}{n !}

The following is the test result:

Click "Test" to begin. \text{Click "Test" to begin.}
What is the Ratio Test?

The Ratio Test is a test used to tell whether an infinite series converges or diverges. Suppose that we have an infinite series ∑an\sum{a_n}. If the limit L=lim⁡n→∞∣an+1an∣L = \lim_{n\to\infty}{|\frac{a_{n+1}}{a_n}|} is less than 1, the series converges. If it is greater than 1, the series diverges. Otherwise, the test is inconclusive.

What does an inconclusive result mean?

An inconclusive result happens when the limit mentioned in the first question, LL, is either 1 or DNE. In that case, the Ratio Test cannot tell you whether that series converges or diverges.

Discover more tools:

lim⁡n→∞∣an∣1n\lim_{n\to\infty} \left|a_n\right|^{\frac{1}{n}} Root Test Calculator
real analysis
∣x−a∣<R|x - a| < R Radius of Convergence Calculator
real analysis
a≤x≤ba \leq x \leq b Interval of Convergence Calculator
real analysis