Determine the convergence of an infinite series involving factorials by applying the Ratio Test.

Vault Of Euclid

Convergence of a Series with Factorials Using the Ratio Test

Sequences core

Determine whether \( \sum_{n=0}^{\infty} \frac{n!}{(2n)!} \) converges.

The solution and a full step-by-step explanation are here. Sign in to read them.

Tests the ability to correctly set up the Ratio Test, simplify expressions with factorials, and evaluate limits of rational functions at infinity.

This is a standard problem in a Calculus II course when learning about convergence tests for infinite series.