Solve for r s=r(((1+i)^n-1)/i)

$s = r (\frac{{(1 + i)}^{n} - 1}{i})$

Step 1

Rewrite the equation as $r (\frac{{(1 + i)}^{n} - 1}{i}) = s$ .

$r (\frac{{(1 + i)}^{n} - 1}{i}) = s$

Step 2

Combine $r$ and $\frac{{(1 + i)}^{n} - 1}{i}$ .

$\frac{r ({(1 + i)}^{n} - 1)}{i} = s$

Step 3

Multiply each term in $\frac{r ({(1 + i)}^{n} - 1)}{i} = s$ by $\frac{i}{{(1 + i)}^{n} - 1}$ to eliminate the fractions.

Multiply each term in $\frac{r ({(1 + i)}^{n} - 1)}{i} = s$ by $\frac{i}{{(1 + i)}^{n} - 1}$ .

$\frac{r ({(1 + i)}^{n} - 1)}{i} \cdot \frac{i}{{(1 + i)}^{n} - 1} = s \frac{i}{{(1 + i)}^{n} - 1}$

Simplify the left side.

Cancel the common factor of ${(1 + i)}^{n} - 1$ .

Factor ${(1 + i)}^{n} - 1$ out of $r ({(1 + i)}^{n} - 1)$ .

$\frac{({(1 + i)}^{n} - 1) r}{i} \cdot \frac{i}{{(1 + i)}^{n} - 1} = s \frac{i}{{(1 + i)}^{n} - 1}$

Cancel the common factor.

$\frac{({(1 + i)}^{n} - 1) r}{i} \cdot \frac{i}{{(1 + i)}^{n} - 1} = s \frac{i}{{(1 + i)}^{n} - 1}$

Rewrite the expression.

$\frac{r}{i} i = s \frac{i}{{(1 + i)}^{n} - 1}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{r}{i} i = s \frac{i}{{(1 + i)}^{n} - 1}$

Rewrite the expression.

$r = s \frac{i}{{(1 + i)}^{n} - 1}$

Simplify the right side.

Combine $s$ and $\frac{i}{{(1 + i)}^{n} - 1}$ .

$r = \frac{s i}{{(1 + i)}^{n} - 1}$