91Ó°ÊÓ

A single card is drawn from a standard deck of 52 cards. Use (9) to find the probability of the given event. Drawing either a 6 or a red card

In Problems 35 and 36 , write out the first five terms of the sequence \(\left\\{a_{n}\right\\}\) if the general term \(a_{n}\) is the \(n\) th digit in the decimal representation of the given number. $$ e $$

Determine whether the given infinite geometric series converges. If convergent, find its sum. $$ \sum_{k=1}^{\infty}(-3)^{k} 7^{-k} $$

Use the Binomial Theorem to expand the given expression. $$ \left(x^{2}-y^{2}\right)^{3} $$

Find the sum of the first 15 terms of the geometric sequence $$ \frac{x}{y},-1, \frac{y}{x}, \ldots $$

Use one or more of the techniques discussed in this section to solve the given counting problem. A pediatrician allows a wellbehaved child to select any 2 of 5 small plastic toys to take home. How many different selections of toys are possible?

Use the Binomial Theorem to expand the given expression. $$ \left(x^{-2}+1\right)^{4} $$

Two dice (red and blue) are rolled. Use (9) to find the probability of the given event. The red die is a 3 , or the total is 5 or 8

Find a formula for the sum of the first \(n\) positive integers: $$ 1+2+3+\cdots+n $$

Determine whether the given infinite geometric series converges. If convergent, find its sum. $$ \sum_{k=1}^{\infty} \pi^{k}\left(\frac{1}{3}\right)^{k-1} $$