Calculus P-Series Test (AI generated)

Calculus P-Series Test (AI generated)

9th - 12th Grade

10 Qs

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Calculus P-Series Test (AI generated)

Calculus P-Series Test (AI generated)

Assessment

Quiz

Mathematics

9th - 12th Grade

Practice Problem

Medium

Created by

Cristen Charnley

Used 3+ times

FREE Resource

AI

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of p for the series ∑(1/n^2) to converge?

p = 0

p = 1

p > 1

p < 1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine whether the series ∑(1/n^3) converges or diverges.

Converges to 0

Diverges

Converges to 1

Converges

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Identify the value of p for the series ∑(1/n^4) to converge.

2

3

4

5

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Does the series ∑(1/n^1/2) converge or diverge? Explain your answer.

Converges

Remains constant

Multiplies by 2

Diverges

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Apply the p-series test to determine the convergence of the series ∑(1/n^3/2).

The series ∑(1/n^3/2) converges.

The series ∑(1/n^3/2) diverges.

The series ∑(1/n^3/2) oscillates.

The p-series test cannot be applied to the given series.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Explain the concept of p-series in calculus.

A p-series in calculus is a series of the form ∑(1/n^p), where n ranges from 1 to 10 and p is a constant. It converges if p > 2 and diverges if p <= 2.

A p-series in calculus is a series of the form ∑(1/n^p), where n ranges from 1 to infinity and p is a variable. It converges if p > 1 and diverges if p <= 1.

A p-series in calculus is a series of the form ∑(1/n^p), where n ranges from 1 to infinity and p is a constant. It converges if p > 1 and diverges if p <= 1.

A p-series in calculus is a series of the form ∑(1/n^p), where n ranges from 1 to infinity and p is a constant. It converges if p > 0 and diverges if p <= 0.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Solve the problem using the p-series test: Determine the convergence of the series ∑(1/n^5).

The series ∑(1/n^5) oscillates.

The series ∑(1/n^5) converges.

The series ∑(1/n^5) diverges.

The series ∑(1/n^5) is undefined.

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