MATH1020U: Sequences and Series - Ratio and Root Tests

What is the definition of a power series?

In a power series, what are the coefficients $c_n$ called?

A power series in (x-a) or centered at/about 'a' has the form ___?

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 is one of the strategies for determining if a given power series converges or diverges?

What is the radius of convergence for the series $\sum_{n=0}^\infty (x-2)^n$?

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 $\sum_{n=0}^\infty \frac{n^2}{7(n+9)}$?

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?

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?

What does the Root Test conclude if $\lim_{n \to \infty} \sqrt[n]{7n}$ is less than 1?

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?

If $\lim_{n \to \infty} (7n)!$ tends to infinity in the Root Test, what conclusion can be made about the series?