Question

The coefficient of 1/x in the expansion of (1+2/x)^3

Answer 1

6

Explanation:

`\left(1+(2)/(x)\right)^3=\sum_(k=0)^3\binom{3}{k}\cdot 1^(3-k)\cdot\left((2)/(x)\right)^k\\ k=1\Rightarrow\binom{3}{1}\cdot 1^(3-1)\cdot\left((2)/(x)\right)^1=(6)/(x)`

Answer 2

Answer 6

Explanation:

We are going to use the formula :

`(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(1+(2)/(x))^3 =1^3+3*1^2*(2)/(x) +3*1*((2)/(x) )^2+((2)/(x))^3\\=1+(6)/(x) +(12)/(x^2) +(8)/(x^3) \\`