Podcast
Questions and Answers
What is the definition of a power series?
What is the definition of a power series?
- A series that involves factorials in each term
- A series that converges for all x values
- A series of the form $\sum_{n=0}^\infty c_nx^n$ (correct)
- A series that converges to a single value
In a power series, what are the coefficients $c_n$ called?
In a power series, what are the coefficients $c_n$ called?
- Coefficients
- Constants (correct)
- Variables
- X-factors
A power series in (x-a) or centered at/about 'a' has the form ___?
A power series in (x-a) or centered at/about 'a' has the form ___?
- $\sum_{n=0}^\infty c_n(a-x)^n$
- $\sum_{n=0}^\infty c_n(x-a)^n$ (correct)
- $\sum_{n=0}^\infty c_n(x+a)^n$
- $\sum_{n=0}^\infty c_nx^n$
At what value is the series $\sum_{n=0}^\infty n(x-6)^n$ centered?
At what value is the series $\sum_{n=0}^\infty n(x-6)^n$ centered?
What values of $x$ make the series $\sum_{n=0}^\infty n!x^n$ converge?
What values of $x$ make the series $\sum_{n=0}^\infty n!x^n$ converge?
What is one of the strategies for determining if a given power series converges or diverges?
What is one of the strategies for determining if a given power series converges or diverges?
What is the radius of convergence for the series $\sum_{n=0}^\infty (x-2)^n$?
What is the radius of convergence for the series $\sum_{n=0}^\infty (x-2)^n$?
For which values of $x$ does the series $\sum_{n=1}^\infty \frac{7}{n} \cos{n}$ converge?
For which values of $x$ does the series $\sum_{n=1}^\infty \frac{7}{n} \cos{n}$ converge?
What is the radius of convergence for the series $\sum_{n=0}^\infty \frac{n^2}{7(n+9)}$?
What is the radius of convergence for the series $\sum_{n=0}^\infty \frac{n^2}{7(n+9)}$?
In the power series $\sum_{n=0}^\infty (8x-3)^n$, what value of R indicates the convergence boundary?
In the power series $\sum_{n=0}^\infty (8x-3)^n$, what value of R indicates the convergence boundary?
For the series $\sum_{n=1}^\infty \frac{7}{n} \cos{n}$, why is it inconclusive at the endpoints of the interval of convergence?
For the series $\sum_{n=1}^\infty \frac{7}{n} \cos{n}$, why is it inconclusive at the endpoints of the interval of convergence?
What does the Ratio Test conclude if $\lim_{n \to \infty} \frac{(-1)^n}{n+3}$ is less than 1?
What does the Ratio Test conclude if $\lim_{n \to \infty} \frac{(-1)^n}{n+3}$ is less than 1?
When does the Ratio Test consider a series absolutely convergent?
When does the Ratio Test consider a series absolutely convergent?
What does the Root Test conclude if $\lim_{n \to \infty} \sqrt[n]{7n}$ is less than 1?
What does the Root Test conclude if $\lim_{n \to \infty} \sqrt[n]{7n}$ is less than 1?
When is the Root Test inconclusive?
When is the Root Test inconclusive?
In the Ratio Test, what conclusion can be drawn if $\lim_{n \to \infty} \frac{(-1)^n}{n+3}$ is greater than 1 or tends to infinity?
In the Ratio Test, what conclusion can be drawn if $\lim_{n \to \infty} \frac{(-1)^n}{n+3}$ is greater than 1 or tends to infinity?
If $\lim_{n \to \infty} (7n)!$ tends to infinity in the Root Test, what conclusion can be made about the series?
If $\lim_{n \to \infty} (7n)!$ tends to infinity in the Root Test, what conclusion can be made about the series?
