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

CAL2.131 Convergence of Series with Exponential Terms Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.131 Convergence of Series with Exponential Terms. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.131 Convergence of Series with Exponential Terms - Select the correct test and conclusion for series containing powers or exponential growth. Standards tags: 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 CAL2.131 Convergence of Series with Exponential Terms skill assessments:

Problem 1Difficulty: Mastery
For sum_{n=1}infty ((n+1)/(n+4))^(n2) 25n, which statement is correct?
AIt converges because (n+1)/(n+4)<1 for every n.
BThe Root Test gives limit e3/25<1, so it converges.
CThe Root Test gives limit 25/e3>1, so the series diverges.
DIt is a p-series with p=3.
Solution & Explanation:The nth-root limit is 25·lim((n+1)/(n+4))n=25/e3. Since this is greater than 1, the Root Test proves divergence.
Problem 2Difficulty: Mastery
For sum_{n=1}infty ((n+1)/(n+4))^(n2) 18n, which statement is correct?
AThe Root Test gives limit 18/e3<1, so the series converges.
BIt diverges because 18n grows exponentially.
CThe Root Test gives limit e3/18>1, so it diverges.
DThe Root Test is inconclusive because (n+1)/(n+4) approaches 1.
Solution & Explanation:The nth root is ((n+1)/(n+4))n·18. Since ((n+1)/(n+4))n -> e-3, the Root Test limit is 18/e3<1.
Problem 3Difficulty: Mastery
For sum_{n=1}infty (7n-5n)/(6n+2n), which statement is correct?
AIt converges because 7n-5n is smaller than 7n.
BIt converges by comparison with sum (6/7)n.
CIt is a p-series with p=7/6.
DIt diverges because the term is comparable to (7/6)n.
Solution & Explanation:The numerator behaves like 7n and the denominator like 6n. Thus the term is comparable to (7/6)n, whose terms do not approach 0.

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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 (Select the correct test and conclusion for series containing powers or exponential growth. Standards tags: 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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