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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) \[\left( x - \frac{1}{x} \right)^{10}\]

 

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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
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