Question

Find the middle term in the expansion of [x-1/x]10

Answer 1

hope u understood my method ...

Answer 2

Answer:

The middle term is -252.

Step-by-step explanation:

The given expression is

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

According to the binomial expansion,

$(a+b)^n=^nC_0a^{n-0}b^0+^nC_1a^{n-1}b^1+...+^nC_na^{n-n}b^n$

The value of n of the given expression is 10. It means the middle term is

$r=\frac{10}{2}=5$

The middle term of the expression is

$^nC_5a^{n-5}b^5=^{10}C_5(x)^{10-5}(\frac{-1}{x})^5$

$^nC_5a^{n-5}b^5=^{10}C_5(x)^{5}(-\frac{1}{x^5})$

$^nC_5a^{n-5}b^5=-\frac{10!}{5!5!}$

$^nC_5a^{n-5}b^5=-252$

Therefore the middle term is -252.