Use the test of your choice to determine whether the following series converge.

$$\sum _ { k = 1 } ^ { \infty } \left( \frac { 1 } { k } + 2 ^ { - k } \right)$$

What are the caveats to conducting t -tests on all of the individual

$$\beta$$

parameters in a multiple-regression model?

Show that $\displaystyle\sum\limits_{n=2}^{\infty}\frac{1}{n\ln n}$ diverges.

(a) Using the integral test.

Use the test of your choice to determine whether the following series converge. $\sum _ { k = 1 } ^ { \infty } \frac { 1 } { \sqrt { k ^ { 3 } - k + 1 } }$

What can you conclude about the convergence or divergence of $\sum a_n$ using the Ratio Test when $a_n$ is a rational function of $n$ ? Explain.

Draw a three-dimensional representation for given molecule. Indicate which ones have a molecular dipole moment and in what direction it is pointing.

$$\mathrm{H}_3 \mathrm{CC} \equiv \mathrm{CCH}_3$$

Use the test of your choice to determine whether the following series converge.

$$\sum _ { k = 2 } ^ { \infty } \frac { 1 } { k ^ { 2 } \ln k }$$

Explain why the integral test cannot be used to decide if the series converges or diverges.

$$\displaystyle\sum\limits_{n=1}^{\infty}n^{2}$$

Use a convergence test of your choice to determine whether the following series converge or diverge.

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

The given figure gives the one-dimensional potential energy well for a 2.0 kg particle (the function U(x) has the form b x^2 ). If yes, at what position, and if no, what is the speed of the particle at x=15 cm ?

Doug Jones submitted his 2018 tax return on time and elected to file a joint tax return with his wife, Darlene. Doug and Darlene did not request an extension for their 2018 tax return. Doug and Darlene owed and paid the IRS $124,000 for their 2018 tax year. Two years later, Doug amended his return and claimed married filing separate status. By changing his filing status, Doug sought a refund for an overpayment for the tax year 2018 (he paid more tax in the original joint return than he owed on a separate return). Is Doug allowed to change his filing status for the 2018 tax year and receive a tax refund with his amended return?

Perform the indicated matrix operations or solve the matrix equation for X given that A, B, and C are defined as follows. If an operation is not defined, state the reason.

$$A = \left[ \begin{array} { r r } { 0 } & { 2 } \\ { - 1 } & { 3 } \\ { 1 } & { 0 } \end{array} \right] \quad B = \left[ \begin{array} { r r } { 4 } & { 1 } \\ { - 6 } & { - 2 } \end{array} \right] \quad C = \left[ \begin{array} { r r } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right]$$

$$2 C - \frac { 1 } { 2 } B$$

The figure shows a unit circle and an angle t whose terminal side is in quadrant III.

If the coordinates of point P_2 are (a, b), explain why the coordinates of point P_1 on the circle and the terminal side of angle t - pi are (-a,-b).

How can a wide gap between rich and poor make it difficult for democracy to flourish?