≥Better Grades
Menu
Worked problem · Calculus II · Units 3B–4B

Ratio Test Example: Worked Example and Solution

A complete course synthesis example with method choice, derivation, verification, and a common wrong approach.

1 problem8 min estimated timeCumulative progression

Problem

  1. Test ∑n=1∞n!/4n\sum_{n=1}^{\infty} n!/4^n.

Complete worked solutions

Every problem has a source-matched answer and independently reviewed derivation.

01

Problem 1: Test ∑n=1∞n!/4n\sum_{n=1}^{\infty} n!/4^n.

Answer: diverges\text{diverges}

Why this method: Course synthesis matches the mathematical structure before any algebraic cleanup.

  1. an+1/an=(n+1)/4a_{n+1}/a_n=(n+1)/4, which eventually exceeds 1, so the positive terms do not approach zero and the series diverges.
  2. The verified result is diverges\text{diverges}.

What is included

See a concise answer and full derivation for test sum from n equals 1 to infinity n ! / 4 to the power (n).

Skills assessed

  • Course synthesis

Prerequisites

  • Calculus II Units 3B through 4B

Common errors

  • Selecting a familiar formula without checking its hypotheses.

Learn fully

Supporting steps