Convergence tests. Game on.

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
Kickoff

3 plays. No signup.

Warm-upeasy

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

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

Mid-gameeasy

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

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

Buzzer beatereasy

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

The 2n2^n in the denominator makes the Ratio test efficient: an+1an→12<1\dfrac{a_{n+1}}{a_n} \to \dfrac{1}{2} < 1.

Overtime

2 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
More Grade 12 skills
Calculus application formulasDegree-radian conversionLaw of sines and cosinesInverse trig domain and rangeMaclaurin seriesPolar and rectangular conversionSpecial limitsStandard antiderivativesAll Grade 12 practice →

Drill it inside a game.

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