Solve a_{n}=2n+1/n

$$a _ { n } = \frac { 2 n + 1 } { n }$$

Solve for n

$$n=\frac{1}{a_{n}-2}$$

$$a_{n}\neq 2$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by n.

$$a_{n}n=2n+1$$

Subtract 2n from both sides.

$$a_{n}n-2n=1$$

Combine all terms containing n.

$$\left(a_{n}-2\right)n=1$$

Divide both sides by a_{n}-2.

$$\frac{\left(a_{n}-2\right)n}{a_{n}-2}=\frac{1}{a_{n}-2}$$

Dividing by a_{n}-2 undoes the multiplication by a_{n}-2.

$$n=\frac{1}{a_{n}-2}$$

Variable n cannot be equal to 0.

$$n=\frac{1}{a_{n}-2}\text{, }n\neq 0$$

Solve for a_n

$$a_{n}=2+\frac{1}{n}$$

$$n\neq 0$$