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Find the Middle Terms(S) in the Expansion Of: (Iii) ( 1 + 3 X + 3 X 2 + X 3 ) 2 N - Mathematics

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

(iii)  \[\left( 1 + 3x + 3 x^2 + x^3 \right)^{2n}\]

 

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Solution

\[(1 + 3x + 3 x^2 + x^3 )^{2n} \]
\[ = (1 + x )^{6n} \]
\[\text{ Here, n is an even number }  . \]
\[ \therefore\text{  Middle term } = \left( \frac{6n}{2} + 1 \right)th = (3n + 1)\text{ th term} \]
\[\text{ Now, we have } \]
\[ T_{3n + 1} \]
\[ = ^{6n}{}{C}_{3n} x^{3n} \]
\[ = \frac{(6n)!}{(3n! )^2} x^{3n}\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.2 | Q 15.03 | Page 38
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