91Ó°ÊÓ

How much do you need to invest now at \(5 \%\) per annum compounded monthly so that in 1 year you will have $$\$ 10,000 ?

True or False A function is a relation between two sets \(D\) and \(R\) so that each element \(x\) in the first set \(D\) is related to exactly one element \(y\) in the second set \(R\)

In Problems 7 -16, show that each sequence is arithmetic. Find the common difference, and list the first four terms. $$ \left\\{s_{n}\right\\}=\\{n+4\\} $$

For a geometric sequence with first term \(a_{1}\) and common ratio \(r,\) where \(r \neq 0, r \neq 1,\) the sum of the first \(n\) terms is \(S_{n}=a_{1} \cdot \frac{1-r^{n}}{1-r}\)

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers \(n\). $$ 1+4+4^{2}+\cdots+4^{n-1}=\frac{1}{3}\left(4^{n}-1\right) $$

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers \(n\). $$ \frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\cdots+\frac{1}{(2 n-1)(2 n+1)}=\frac{n}{2 n+1} $$

Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers \(n\). $$ 4+3+2+\cdots+(5-n)=\frac{1}{2} n(9-n) $$

Find the fifth term and the nth term of the geometric sequence whose first term \(a_{1}\) and common ratio \(r\) are given. $$ a_{1}=2 ; \quad r=3 $$

Find the fifth term and the nth term of the geometric sequence whose first term \(a_{1}\) and common ratio \(r\) are given. $$ a_{1}=-2 ; \quad r=4 $$

Find the fifth term and the nth term of the geometric sequence whose first term \(a_{1}\) and common ratio \(r\) are given. $$ a_{1}=5 ; \quad r=-1 $$