Explain the following: The Root Test.

Describe: The Alternating Series Test.

Use the Ratio Test or the Root Test to determine the convergence or divergence of the series.

$$\sum_{n=0}^{\infty} \frac{7^n}{(2 n+3)^n}$$

Use the Root Test to determine whether the following series converge.

$$\sum _ { k = 1 } ^ { \infty } \frac { k } { e ^ { k } }$$

Let

$$A=\left[\begin{array}{lll}a & b & c \\ p & q & r \\ x & y & z\end{array}\right]$$

and let

$$P=\left[\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right]$$

. Thus $P$ is a permutation matrix whose rows are those of the $3 \times 3$ identity matrix in the order $2,3,1$. Compute $P A P^T$ and compare with $A$.

Complete the following statements with the best answer.

To test the hypothesis $H_0: \mu \leq 87$, one would use a(n) $\underline{\qquad \qquad}$-tailed test.

How do you test for lipids?

Use the Ratio Test or the Root Test to determine whether the following series converge absolutely or diverge. $\sum_{k=1}^{\infty} \frac{k^{2}}{4^{k}}$

Passing Grade There are 40 students in your class. On one test, $95 \%$ of the students received passing grades. How many students failed the test?

How many different tests can be made from a test bank of 20 questions if the test consists of 5 questions?

What is the ELISA test used for?

How are the F test values computed?

The Root Test Use the Root Test to determine whether the following series converge.
$\sum_{k=1}^{\infty}\left(\frac{k+1}{2 k}\right)^k$

Use the ratio test to determine whether the series converges. If the test is inconclusive, then say so.

$$\sum_{k=1}^{\infty} \frac{1}{5 k}$$