Finite Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply the numerator and denominator of $\frac{{(1 + i)}^{- (n - 1)}}{i}$ by the conjugate of $i$ to make the denominator real.

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

Step 1.1.2

Multiply.

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Step 1.1.2.1

Combine.

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

Step 1.1.2.2

Simplify the numerator.

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Step 1.1.2.2.1

Apply the distributive property.

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

Step 1.1.2.2.2

Multiply $- 1$ by $- 1$ .

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

Step 1.1.2.2.3

Reorder factors in ${(1 + i)}^{- n + 1} i$ .

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

Step 1.1.2.3

Simplify the denominator.

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Step 1.1.2.3.1

Raise $i$ to the power of $1$ .

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

Step 1.1.2.3.2

Raise $i$ to the power of $1$ .

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

Step 1.1.2.3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.1.2.3.4

Add $1$ and $1$ .

$p = r + r (1 - \frac{i {(1 + i)}^{- n + 1}}{i^{2}})$

Step 1.1.2.3.5

Rewrite $i^{2}$ as $- 1$ .

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

Step 1.1.3

Move the negative one from the denominator of $\frac{i {(1 + i)}^{- n + 1}}{- 1}$ .

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

Step 1.1.4

Rewrite $- 1 \cdot (i {(1 + i)}^{- n + 1})$ as $- (i {(1 + i)}^{- n + 1})$ .

$p = r + r (1 - - (i {(1 + i)}^{- n + 1}))$

Step 1.1.5

Multiply $- (- i {(1 + i)}^{- n + 1})$ .

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Step 1.1.5.1

Multiply $- 1$ by $- 1$ .

$p = r + r (1 + 1 (i {(1 + i)}^{- n + 1}))$

Step 1.1.5.2

Multiply ${(1 + i)}^{- n + 1}$ by $1$ .

$p = r + r (1 + {(1 + i)}^{- n + 1} i)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Multiply $r$ by $1$ .

$p = r + r + r ({(1 + i)}^{- n + 1} i)$

Step 1.4

Rewrite using the commutative property of multiplication.

$p = r + r + i r {(1 + i)}^{- n + 1}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $r$ and $r$ .

$p = 2 r + i r {(1 + i)}^{- n + 1}$

Step 2.2

Reorder $i$ and $r$ .

$p = 2 r + r i {(1 + i)}^{- n + 1}$