Solve S_{n}=n/n+1

$$S _ { n } = \frac { n } { n + 1 }$$

Solve for n

$$n=-\frac{S_{n}}{S_{n}-1}$$

$$S_{n}\neq 1$$

Steps for Solving Linear Equation

Variable n cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by n+1.

$$S_{n}\left(n+1\right)=n$$

Use the distributive property to multiply S_{n} by n+1.

$$S_{n}n+S_{n}=n$$

Subtract n from both sides.

$$S_{n}n+S_{n}-n=0$$

Subtract S_{n} from both sides. Anything subtracted from zero gives its negation.

$$S_{n}n-n=-S_{n}$$

Combine all terms containing n.

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

Divide both sides by S_{n}-1.

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

Dividing by S_{n}-1 undoes the multiplication by S_{n}-1.

$$n=-\frac{S_{n}}{S_{n}-1}$$

Variable n cannot be equal to -1.

$$n=-\frac{S_{n}}{S_{n}-1}\text{, }n\neq -1$$

Solve for S_n

$$S_{n}=\frac{n}{n+1}$$

$$n\neq -1$$