# Find the Middle Terms(S) in the Expansion Of: (I) ( X − 1 X ) 10 - Mathematics

Find the middle terms(s) in the expansion of:

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

#### Solution

(i) $\left( x - \frac{1}{x} \right)^{10}$
$\text{ Here, n is an even number } .$
$\therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right) \text{ th = 6th term }$
$\text{ Now, we have }$
$T_6 = T_{5 + 1}$
$=^{10}{}{C}_5 x^{10 - 5} \left( \frac{- 1}{x} \right)^5$
$= - \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2}$
$= - 252$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 15.01 | Page 38