Question

the coefficient of 1/x^4 in the expansion of (x+1/x)^10 is?​

Answer 1

Step-by-step explanation:

We have,

$(x + \frac{1}{x} )^{10}$

General term

$t_{r + 1} = \:^{10}C_{r}. {x}^{10 - r} . {x}^{ - r}$

$\implies t_{r + 1} = \:^{10}C_{r}. {x}^{10 - 2r}$

Now,

$10 - 2r = - 4$

$\implies \: r = 7$

so, coefficient of $( \frac{1}{x})^{4}$ is

$\: ^{10} C_{7}$

$= \:^{10} C_{3} = 120$