91Ó°ÊÓ

Using Mathematical Induction In Exercises \(11-24,\) use mathematical induction to prove the formula for every positive integer \(n .\) $$1+4+7+10+\cdots+(3 n-2)=\frac{n}{2}(3 n-1)$$

Find the sample space for the experiment. A sales representative makes presentations about a product in three homes per day. In each home, there may be a sale (denote by S) or there may be no sale (denote by F).

Finding a Binomial Coefficient In Exercises \(5-14\) , find the binomial coefficient. $$\cdot \left( \begin{array}{c}{100} \\ {2}\end{array}\right)$$

Writing the Terms of a Geometric Sequence, write the first five terms of the geometric sequence. $$ a_{1}=8, r=2 $$

Writing the Terms of a Sequence In Exercises \(7-22,\) write the first five terms of the sequence. (Assume that \(n\) begins with \(1 .\) ) $$ a_{n}=\frac{(-1)^{n}}{n^{2}} $$

Using Pascal's Triangle In Exercises 15-18, evaluate using Pascal's Triangle. $$\left( \begin{array}{l}{6} \\ {5}\end{array}\right)$$

Writing the Terms of a Geometric Sequence, write the first five terms of the geometric sequence. $$ a_{1}=1, r=\frac{1}{2} $$

Using Mathematical Induction In Exercises \(11-24,\) use mathematical induction to prove the formula for every positive integer \(n .\) $$1+2+2^{2}+2^{3}+\cdots+2^{n-1}=2^{n}-1$$

Find the probability for the experiment of tossing a coin three times. Use the sample space \(S=H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T.\) The probability of getting exactly one tail

Writing the Terms of a Sequence In Exercises \(7-22,\) write the first five terms of the sequence. (Assume that \(n\) begins with \(1 .\) ) $$ a_{n}=\frac{2^{n}}{3^{n}} $$