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Write the Middle Term in the Expansion of ( X + 1 X ) 10 - Mathematics

Write the middle term in the expansion of  \[\left( x + \frac{1}{x} \right)^{10}\]

 
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Solution

\[\text{ Here, n, i . e . , 10, is an even number } \]

\[ \therefore \text{ Middle term } = \left( \frac{10}{2} + 1 \right)\text{ th term = 6th term } \]

\[\text{ Thus, we have: } \]

\[ T_6 = T_{5 + 1} \]

\[ = ^{10}{}{C}_5 \left( x \right)^{10 - 5} \times \left( \frac{1}{x} \right)^5 \]

\[ = ^{10}{}{C}_5 \]

 

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Q 8 | Page 45
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