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Worked problem · Calculus II · Units 3B–4B

Alternating Series 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∞(−1)n−1/n\sum_{n=1}^{\infty}(-1)^{n-1}/n.

Complete worked solutions

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

01

Problem 1: Test ∑n=1∞(−1)n−1/n\sum_{n=1}^{\infty}(-1)^{n-1}/n.

Answer: converges conditionally\text{converges conditionally}

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

  1. 1/n1/n decreases to zero, so the alternating-series test gives convergence; ∑1/n\sum1/n diverges, hence convergence is conditional.
  2. The verified result is converges conditionally\text{converges conditionally}.

What is included

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

Skills assessed

  • Course synthesis

Prerequisites

  • Calculus II Units 3B through 4B

Common errors

  • Selecting a familiar formula without checking its hypotheses.

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Supporting steps