What is expand (1-1/x)^5 ?

The solution to expand (1-1/x)^5 is 1-5/x+(10)/(x^2)-(10)/(x^3)+5/(x^4)-1/(x^5)

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expand (1-1/x)^5

expand

(1 - \frac{1}{x})^{5}

1 - \frac{5}{x} + \frac{10}{x ^{2}} - \frac{10}{x ^{3}} + \frac{5}{x ^{4}} - \frac{1}{x ^{5}}

Solution steps

(1 - \frac{1}{x})^{5}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = - \frac{1}{x}

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (- \frac{1}{x})^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- \frac{1}{x})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (- \frac{1}{x})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- \frac{1}{x})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- \frac{1}{x})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (- \frac{1}{x})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- \frac{1}{x})^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (- \frac{1}{x})^{0} : 1

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 1^{4} (- \frac{1}{x})^{1} : - \frac{5}{x}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (- \frac{1}{x})^{2} : \frac{10}{x ^{2}}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (- \frac{1}{x})^{3} : - \frac{10}{x ^{3}}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (- \frac{1}{x})^{4} : \frac{5}{x ^{4}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (- \frac{1}{x})^{5} : - \frac{1}{x ^{5}}

= 1 - \frac{5}{x} + \frac{10}{x ^{2}} - \frac{10}{x ^{3}} + \frac{5}{x ^{4}} - \frac{1}{x ^{5}}

(1 + h)^{4}

\frac{1}{4} + \frac{5}{8}

\frac{2}{3} \cdot \frac{5}{7}

\frac{x 7}{3}

9 x + 9 - 1

What is expand (1-1/x)^5 ?
The solution to expand (1-1/x)^5 is 1-5/x+(10)/(x^2)-(10)/(x^3)+5/(x^4)-1/(x^5)