Give the expansion of the binomial. Simplify your answer.

a. $(a+b)^3$

b. $(20+1)^3$

c. $(20-1)^3$

a. In how many ways can a club with 20 members choose a president and a vice president?

b. In how many ways can the club choose a 2-person governing council?

Study Pascal's triangle. Describe the symmetry that the numbers in the triangle have.

Of the 320 children at a movie, 190 buy popcorn and 245 buy something to drink. If 151 children buy both, how many buy neither?

Find the number of permutations of the letters.

a. MALE

b. MALL

A certain small college has 1000 students. Let F= the set of college freshmen, and let M= the set of music majors. Describe the following set in words and tell how many members it has.

$$F \cap M$$

Draw a Venn diagram and shade the region representing the set given in part (a). Then draw a separate Venn diagram and shade the region representing the set given in part (b).

a. $P \cap Q$

b. $P \cup Q$

Find the value of expression.

a. ${ }_5 P_2$

b. ${ }_5 C_2$

Find the value of expression.

a. ${ }_5 P_2$

b. ${ }_5 C_2$

Determine whether the series is convergent or divergent. \

$$\sum_{n=1}^{\infty} \dfrac{n}{n^2+1}$$

Find the first six partial sums of the following infinite series. If the sums have a finite limit, write “convergent.” If not, write “divergent.”

$$1-0.7-0.07-0.007-0.0007-...$$

Using apostrophes correctly, write the singular possessive and the plural possessive of the following nouns. Example 1. girl $\underline{\text{\color{#c34632}girl’s}}$ $\underline{\text{\color{#c34632}girls’}}$

lady ________ ________

Assuming each function can be represented by a power series, find the Maclaurin expansion of each function. $f(x)=e^{2 x}$

A $0.50~\mu \mathrm{F}$ and a $1.4~\mu \mathrm{F}$ capacitor are connected in series to a $9.0~\mathrm{V}$ battery. Calculate the charge on each.