91Ó°ÊÓ

Use a graphing calculator to do the following. (a) Find the first 10 terms of the sequence. (b) Graph the first 10 terms of the sequence. $$a_{n}=\frac{12}{n}$$

Prove that \(n<2^{n}\) for all natural numbers \(n .\)

Interest Rate John buys a stereo system for \(\$ 640 .\) He agrees to pay \(\$ 32\) a month for 2 years. Assuming that interest is compounded monthly, what interest rate is he paying?

Evaluate the expression. $$\left(\begin{array}{l} 5 \\ 0 \end{array}\right)+\left(\begin{array}{l} 5 \\ 1 \end{array}\right)+\left(\begin{array}{l} 5 \\ 2 \end{array}\right)+\left(\begin{array}{l} 5 \\ 3 \end{array}\right)+\left(\begin{array}{l} 5 \\ 4 \end{array}\right)+\left(\begin{array}{l} 5 \\ 5 \end{array}\right)$$

Find the first five terms of the sequence and determine if it is arithmetic. If it is arithmetic, find the common difference and express the \(n\) th term of the sequence in the standard form $$a_{n}=a+(n-1) d$$ $$a_{n}=\frac{1}{1+2 n}$$

Prove that \((n+1)^{2}<2 n^{2}\) for all natural numbers \(n \geq 3\)

Evaluate the expression. $$\left(\begin{array}{l} 5 \\ 0 \end{array}\right)-\left(\begin{array}{l} 5 \\ 1 \end{array}\right)+\left(\begin{array}{l} 5 \\ 2 \end{array}\right)-\left(\begin{array}{l} 5 \\ 3 \end{array}\right)+\left(\begin{array}{l} 5 \\ 4 \end{array}\right)-\left(\begin{array}{l} 5 \\ 5 \end{array}\right)$$

Use a graphing calculator to do the following. (a) Find the first 10 terms of the sequence. (b) Graph the first 10 terms of the sequence. $$a_{n}=4-2(-1)^{n}$$

Find the first five terms of the sequence and determine if it is arithmetic. If it is arithmetic, find the common difference and express the \(n\) th term of the sequence in the standard form $$a_{n}=a+(n-1) d$$ $$a_{n}=1+\frac{n}{2}$$

Use the Binomial Theorcm to expand the expression. $$(x+2 y)^{4}$$