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

CAL2.115 Telescoping 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 CAL2.115 Telescoping Series. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.115 Telescoping Series - Select the correct cancellation pattern and sum for a telescoping 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

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 CAL2.115 Telescoping Series skill assessments:

Problem 1Difficulty: Mastery

Evaluate sum_{n=1}^infinity (1/(n²+n+1) - 1/(n²+3n+3)).

AThe sum is 0 because the two denominators have the same leading term.

BThe sum is 1/7 because the second denominator at n = 1 is 7.

CThe series diverges because the terms are rational but not partial fractions.

DThe second denominator is (n+1)² + (n+1) + 1, so the series is A_n - A_{n+1} and sums to A_1 = 1/3.

Solution & Explanation:Let A_n = 1/(n²+n+1). Then the second fraction is A_{n+1}. The partial sums are A_1 - A_{N+1}, and A_{N+1} tends to 0.

Problem 2Difficulty: Mastery

Let f(n) = (n+1)/(n²+1). Evaluate sum_{n=1}^infinity (f(n) - f(n+1)).

AThe sum is 0 because f(n) and f(n+1) both tend to 0.

BThe sum is f(2) = 3/5 because the second term appears in the formula.

CS_N = f(1) - f(N+1), and since f(1) = 1 and f(N+1) -> 0, the sum is 1.

DThe series diverges because f(n) is not a rational partial fraction in n.

Solution & Explanation:A telescoping series keeps the first endpoint and the limiting tail. The tail goes to 0, so the value is f(1) = 1.

Problem 3Difficulty: Mastery

For real a with positive denominators and positive integer k, evaluate sum_{n=1}^infinity k/((n+a)(n+a+k)).

AIt equals (1/k)sum_{j=1}^k 1/(a+j).

BIt equals sum_{j=1}^k 1/(a+j), since k/((n+a)(n+a+k)) = 1/(n+a) - 1/(n+a+k).

CIt equals only 1/(a+1).

DIt diverges because each term contains 1/(n+a).

Solution & Explanation:The numerator k matches the separation of the two factors. A k-step shift leaves exactly the k front endpoint terms.

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Frequently Asked Questions

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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 cancellation pattern and sum for a telescoping 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.).