To what number does the series $\sum \underset{}{k=0}\stackrel{}{\infty }{\left(-\frac{1}{2}\right)}^k$ converge?

6) Use the Intermediate Value Theorem to show that the equation $x^2-6x-3=0$ has a solution on the interval $[0,7]$. Which of the following justifies the existence of a solution?

Suppose the average rate of change of $g\left(x\right)$ between $x=4$ and $x=7$ is $0$. Which statement must be true?

For which values of $p$ does the series $\sum _{n=1}^{\infty }\frac{{(-1)}^{n+1}}{n^p}$ converge?

Which of the following definite integrals is equal to $\underset{n\to \infty }{lim}\sum \frac{10}{n}(1+\frac{5k}{n}{)}^2(k=1n)$?

For which positive integers $k$ is the following series convergent? $\sum n_1\infty \frac{{(n!)}^2}{(kn)!}$

Which of the following statements about the series $\sum \underset{}{n=1}\infty \frac{1}{2^n}$ is true?

For which values of p does the improper integral ${\int }_1^{\infty }{x}^{3p+1} dx$ converge?

The graph of $y=f\left(x\right)$ is shown above. What is $\underset{x\to 1}{lim}f\left(x\right)$?