What is expand (2+1/x)^5 ?

The solution to expand (2+1/x)^5 is 32+(80)/x+(80)/(x^2)+(40)/(x^3)+(10)/(x^4)+1/(x^5)

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expand (2+1/x)^5

expand

(2 + \frac{1}{x})^{5}

32 + \frac{80}{x} + \frac{80}{x ^{2}} + \frac{40}{x ^{3}} + \frac{10}{x ^{4}} + \frac{1}{x ^{5}}

Solution steps

(2 + \frac{1}{x})^{5}

Apply binomial theorem:

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

a = 2, b = \frac{1}{x}

= i = 0 \sum 5 (i 5) \cdot 2^{(5 - i)} (\frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 2^{5} (\frac{1}{x})^{0} : 32

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} \cdot 2^{4} (\frac{1}{x})^{1} : \frac{80}{x}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 2^{3} (\frac{1}{x})^{2} : \frac{80}{x ^{2}}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 2^{2} (\frac{1}{x})^{3} : \frac{40}{x ^{3}}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 2^{1} (\frac{1}{x})^{4} : \frac{10}{x ^{4}}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 2^{0} (\frac{1}{x})^{5} : \frac{1}{x ^{5}}

= 32 + \frac{80}{x} + \frac{80}{x ^{2}} + \frac{40}{x ^{3}} + \frac{10}{x ^{4}} + \frac{1}{x ^{5}}

(z - \frac{1}{2}) (z - \frac{1}{4})

\frac{d}{d x} ((x + 3) sin (x)) - x^{2} + 3

(x - 2) x

- 5 x - (- 68)

\frac{- 1 + cos ( x )}{( ( 1 - cos ( x ) ) ^{2} + sin ^{2} ( t ) )}

What is expand (2+1/x)^5 ?
The solution to expand (2+1/x)^5 is 32+(80)/x+(80)/(x^2)+(40)/(x^3)+(10)/(x^4)+1/(x^5)