AP Calculus BC Practice Questions

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Which of the following series converges for all real numbers x?

$\sum \frac{1}{n^2}$ (correct)

$\sum \frac{1}{2^n}$

$\sum \frac{1}{n}$

$\sum \frac{1}{n^3}$

What are all values of x for which the series converges?

|x| > 3

|x| = 3

All x except x = 0 (correct)

|x| = 2

Which of the following series can be used with the limit comparison test to determine convergence or divergence?

$\sum \frac{1}{n^4}$ (correct)

$\sum \frac{1}{n^3}$

$\sum \frac{1}{n!}$

$\sum \frac{1}{2^n}$

Which of the following series diverges?

$\sum \frac{1}{n!}$ Signup and view all the answers

Which of the following series can be used with the limit comparison test to determine convergence or divergence?

$\sum \frac{1}{n^3}$ Signup and view all the answers

What are all values of x for which the series diverges?

|x| > 3 Signup and view all the answers

If the series $\sum_{n=1}^\infty \frac{1}{n^p}$ converges, what are all values of p for which this is true?

$p < 1$ Signup and view all the answers

If $f$ is a positive, continuous, decreasing function and the series $\sum_{n=1}^\infty f(n)$ converges, which of the following statements about the function $f$ must be true?

$f(x)$ has a limit of 0 Signup and view all the answers

Consider the infinite series $\sum_{n=1}^\infty g(n)$. If the integral test can be used to verify convergence because $g(x)$ is positive, continuous, and decreasing, which inequality is true?

$\frac{dg}{dx} < 0$ Signup and view all the answers

The integral test can be used to determine which of the following statements about an infinite series is true?

The series diverges because $\int g(x)dx > 0$ Signup and view all the answers

If $\sum_{n=1}^\infty h(n)$ is an infinite series where $h(n)$ has no finite limit, what conclusions can be drawn using the integral test?

The series diverges, and terms have a limit of 0. Signup and view all the answers

If $f$ is a positive, continuous, decreasing function and $\sum_{n=1}^\infty f(n)$ converges to k, what must be true about this convergence?

$k$ converges Signup and view all the answers

What must be true if the series converges for all n?

The series converges for all n Signup and view all the answers

For the infinite series with nth partial sum for $a_n$, what is the sum of the series?

$a_n$ Signup and view all the answers

Consider the sequence $a_n$ and the infinite series. Which of the following is true?

$a_n$ diverges and the series diverges Signup and view all the answers

AP Calculus BC Practice Questions

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Questions and Answers

Which of the following series converges for all real numbers x?

What are all values of x for which the series converges?

Which of the following series can be used with the limit comparison test to determine convergence or divergence?

Which of the following series diverges?

Which of the following series can be used with the limit comparison test to determine convergence or divergence?

What are all values of x for which the series diverges?

If the series $\sum_{n=1}^\infty \frac{1}{n^p}$ converges, what are all values of p for which this is true?

If $f$ is a positive, continuous, decreasing function and the series $\sum_{n=1}^\infty f(n)$ converges, which of the following statements about the function $f$ must be true?

Consider the infinite series $\sum_{n=1}^\infty g(n)$. If the integral test can be used to verify convergence because $g(x)$ is positive, continuous, and decreasing, which inequality is true?

The integral test can be used to determine which of the following statements about an infinite series is true?

If $\sum_{n=1}^\infty h(n)$ is an infinite series where $h(n)$ has no finite limit, what conclusions can be drawn using the integral test?

If $f$ is a positive, continuous, decreasing function and $\sum_{n=1}^\infty f(n)$ converges to k, what must be true about this convergence?

What must be true if the series converges for all n?

For the infinite series with nth partial sum for $a_n$, what is the sum of the series?

Consider the sequence $a_n$ and the infinite series. Which of the following is true?

If $p > 1$ for $rac{1}{n^p}$, which of the following statements about the infinite series is true?

Which of the following series diverge?

Which term test can be used to determine divergence for the given series?

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