Solve P=R(1-(1+1)^-n/1)

$$P = R ( \frac { 1 - ( 1 + 1 ) ^ { - n } } { 1 } )$$

Solve for R

$$\left\{\begin{matrix}R=-\frac{P\times 2^{n}}{1-2^{n}}\text{, }&n\neq 0\\R\in \mathrm{R}\text{, }&P=0\text{ and }n=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Add 1 and 1 to get 2.

$$P=R\times \frac{1-2^{-n}}{1}$$

Anything divided by one gives itself.

$$P=R\left(1-2^{-n}\right)$$

Swap sides so that all variable terms are on the left hand side.

$$R\left(1-2^{-n}\right)=P$$

Use the distributive property to multiply R by 1-2^{-n}.

$$R-R\times 2^{-n}=P$$

Combine all terms containing R.

$$\left(1-2^{-n}\right)R=P$$

The equation is in standard form.

$$\left(-\frac{1}{2^{n}}+1\right)R=P$$

Divide both sides by 1-2^{-n}.

$$\frac{\left(-\frac{1}{2^{n}}+1\right)R}{-\frac{1}{2^{n}}+1}=\frac{P}{-\frac{1}{2^{n}}+1}$$

Dividing by 1-2^{-n} undoes the multiplication by 1-2^{-n}.

$$R=\frac{P}{-\frac{1}{2^{n}}+1}$$

Divide P by 1-2^{-n}.

$$R=\frac{P\times 2^{n}}{2^{n}-1}$$

Solve for P

$$P=-\frac{R}{2^{n}}+R$$