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

CAL2.139 Power Series from Geometric Series Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.139 Power Series from Geometric Series. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.116 Geometric Series - Choose whether a geometric series converges and, if it does, select its sum. 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

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.139 Power Series from Geometric Series skill assessments:

Problem 1Difficulty: Mastery
Which statement correctly describes \(\sum_{n=0}\infty \left(\frac{x2-1}{3}\right)n\)?
AConverges for \(-32}\)
BConverges for \(-22}\)
CConverges for \(∣x∣ >2\); sum = \(\frac{3}{4-x2}\)
DDiverges for \(-2
Solution & Explanation:The ratio is \((x2-1)/3\). The inequality \(∣x2-1∣ <3\) gives \(x2<4\), so \(-22-1)/3)=3/(4-x2)\).
Problem 2Difficulty: Mastery
For \(\sum_{n=1}\infty \left(\frac{x-2}{x}\right)n\), choose the correct convergence set and sum.
AConverges for \(x>1\); sum = \(\frac{x-2}{2}\)
BConverges for \(x<1\); sum = \(\frac{x-2}{2}\)
CConverges for \(x>1\); sum = \(\frac{x}{2}\)
DDiverges for all \(x\)
Solution & Explanation:The ratio is \((x-2)/x\). The condition \(∣x-2∣ <∣x∣\) simplifies to \(x>1\). Since the series starts at \(n=1\), the sum is \(r/(1-r)=((x-2)/x)/(2/x)=(x-2)/2\).
Problem 3Difficulty: Mastery
For \(\sum_{n=0}\infty \left(\frac{1}{x+1}\right)n\), choose the correct convergence set and sum.
AConverges for \(-2
BConverges for all \(x\ne -1\); sum = \(\frac{x+1}{x}\)
CConverges for \(x<-2\) or \(x>0\); sum = \(\frac{x}{x+1}\)
DConverges for \(x<-2\) or \(x>0\); sum = \(\frac{x+1}{x}\)
Solution & Explanation:The ratio is \(1/(x+1)\). Convergence requires \(∣1/(x+1)∣ <1\), so \(∣x+1∣ >1\), meaning \(x<-2\) or \(x>0\). The sum is \(1/(1-1/(x+1))=(x+1)/x\).

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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 a geometric series converges and, if it does, select its sum. 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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