Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55

CAL2.124 Alternating Series Test Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.124 Alternating Series Test. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.124 Alternating Series Test - Choose whether an alternating series converges using decreasing positive terms approaching zero. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related CAL2.124 Alternating Series Test skill assessments:

Problem 1Difficulty: Mastery
Which series can be proven to converge by the Alternating Series Test?
A∑_{n=1}^∞ (-1)n n/(n+1)
B∑_{n=1}^∞ (-1)n(3 + (-1)n)/n
C∑_{n=3}^∞ (-1)n ln(n+1)/√(n+1)
D∑_{n=1}^∞ (-1)n cos(1/n)
Solution & Explanation:In choice C, the magnitude ln(n+1)/√(n+1) approaches 0 and is eventually decreasing. Choice A and D fail the zero-limit condition, while choice B has positive magnitudes that are not eventually nonincreasing.
Problem 2Difficulty: Mastery
For real c, assume n2 + n + c is nonzero for the terms being used. What does the Alternating Series Test say about ∑_{n=1}^∞ (-1)n (n2+1)/(n2+n+c)?
AIt applies for c > 0.
BIt applies for c < 0.
CIt never proves convergence because the magnitude approaches 1.
DIt applies for every c because the signs alternate.
Solution & Explanation:The leading terms in the numerator and denominator are both n2, so the magnitude approaches 1 for every fixed c. The zero-limit condition fails, so the Alternating Series Test cannot prove convergence and the series diverges.
Problem 3Difficulty: Mastery
For which real s does the Alternating Series Test apply to ∑_{n=1}^∞ (-1)n /(ns + n)?
Aall real s
Bs > 0 only
Cs ≥ 1 only
Ds < 0 only
Solution & Explanation:For any fixed real s, ns + n is eventually positive and grows without bound, so its reciprocal tends to 0 and is eventually decreasing. Finite early behavior does not prevent applying the test to a tail.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55 (Choose whether an alternating series converges using decreasing positive terms approaching zero. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.IF; CCSS.MP2, MP3, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-SER; TEKS 19 TAC section 111.55.).

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