Grade 12 · Algebra & functions

Convergence tests practice

Convergence tests is a grade 12 math skill: apply convergence tests (ratio, comparison, alternating series) to determine whether an infinite series converges. Below are 3 practice questions with answers and step-by-step explanations, drawn from the 5 convergence tests problems our math games drill.

5 questions in the bank

Sample questions

Try 3 for free

Question 1easy

The harmonic series $\displaystyle\sum \dfrac{1}{n}$ is:

The harmonic series is a p-series with $p = 1$ . Since $p \le 1$ , it diverges.

Question 2easy

Which test is best for $\displaystyle\sum \dfrac{n!}{n^n}$ ?

Factorials in the numerator make the Ratio test the natural choice.

Question 3easy

Which test should you try first for $\displaystyle\sum \dfrac{1}{n \cdot 2^n}$ ?

The $2^n$ in the denominator makes the Ratio test efficient: $\dfrac{a_{n+1}}{a_n} \to \dfrac{1}{2} < 1$ .

More Grade 12 skills:

Calculus application formulas Degree-radian conversion Law of sines and cosines Inverse trig domain and range Maclaurin series Polar and rectangular conversion Special limits Standard antiderivatives All Grade 12 practice →

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