simplify (i/n-1)^3

Solution

simplify

(\frac{i}{n} - 1)^{3}

- \frac{n ^{2} - 3}{n ^{2}} + \frac{- 1 + 3 n ^{2}}{n ^{3}} i

Solution steps

(\frac{i}{n} - 1)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(\frac{i}{n} - 1)^{3} = (\frac{i}{n})^{3} - 3 (\frac{i}{n})^{2} \cdot 1 + 3 \cdot \frac{i}{n} \cdot 1^{2} - 1^{3}

= (\frac{i}{n})^{3} - 3 (\frac{i}{n})^{2} \cdot 1 + 3 \cdot \frac{i}{n} \cdot 1^{2} - 1^{3}

Simplify

(\frac{i}{n})^{3} - 3 (\frac{i}{n})^{2} \cdot 1 + 3 \cdot \frac{i}{n} \cdot 1^{2} - 1^{3} : - \frac{i}{n ^{3}} + 3 \cdot \frac{1}{n ^{2}} + 3 \cdot \frac{i}{n} - 1

= - \frac{i}{n ^{3}} + 3 \cdot \frac{1}{n ^{2}} + 3 \cdot \frac{i}{n} - 1

Simplify

- \frac{i}{n ^{3}} + 3 \cdot \frac{1}{n ^{2}} + 3 \cdot \frac{i}{n} - 1 : - \frac{n ^{2} - 3}{n ^{2}} + \frac{- 1 + 3 n ^{2}}{n ^{3}} i

= - \frac{n ^{2} - 3}{n ^{2}} + \frac{- 1 + 3 n ^{2}}{n ^{3}} i

2 (7 + 11)

\frac{1}{( 2 ( n + 1 ) ) !}

(3 x + 2)^{2}

(1 - L) \cdot (1 - t) \cdot w \cdot L

(9 - e)^{3}

What is (i/n-1)^3 ?
The solution to (i/n-1)^3 is -(n^2-3)/(n^2)+(-1+3n^2)/(n^3)i