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

CAL2.134 Selecting a Convergence 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 CAL2.134 Selecting a Convergence Test. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.134 Selecting a Convergence Test - Choose the most appropriate convergence test based on the structure of a given series. 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 CAL2.134 Selecting a Convergence Test skill assessments:

Problem 1Difficulty: Mastery
For the positive series ∑_{n=1}∞ ((4n2+1)/(4n2+5n))n, which test should be selected first?
ARoot Test only
BRatio Test only
Cnth-Term Divergence Test after evaluating the term limit
Dp-Series Test
Solution & Explanation:The root test gives a limiting root of 1, so it is inconclusive. The term itself approaches e^(-5/4), not 0, making the nth-Term Divergence Test decisive.
Problem 2Difficulty: Mastery
For the series ∑_{n=1}∞ (-1)n (n2+1)/(n4+1), which test is most efficient to prove convergence?
AAlternating Series Test
BDirect Comparison Test on absolute values
Cnth-Term Divergence Test
DRoot Test
Solution & Explanation:The absolute value is at most a constant multiple of 1/n2 for large n, so Direct Comparison proves absolute convergence. That is stronger and cleaner than relying only on alternating signs.
Problem 3Difficulty: Mastery
For the positive series ∑_{n=2}∞ 1/n^(1+1/n), which test most directly compares it to ∑1/n?
ALimit Comparison Test
BRatio Test
CRoot Test
DGeometric Series Test
Solution & Explanation:The ratio of 1/n^(1+1/n) to 1/n is n^(-1/n), which approaches 1. Limit Comparison with the harmonic series is the appropriate test.

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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 the most appropriate convergence test based on the structure of a given series. 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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