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प्रश्न
Find the 4th term from the beginning and 4th term from the end in the expansion of \[\left( x + \frac{2}{x} \right)^9\] .
उत्तर
Let Tr+1 be the 4th term from the end.
Then, Tr+1 is (10 − 4 + 1)th, i.e., 7th, term from the beginning.
\[\therefore T_7 = T_{6 + 1} \]
\[ = ^{9}{}{C}_6 \left( x^{9 - 6} \right) \left( \frac{2}{x} \right)^6 \]
\[ = \frac{9 \times 8 \times 7}{3 \times 2}\left( x^3 \right)\left( \frac{64}{x^6} \right)\]
\[ = \frac{5376}{x^3}\]
4th term from the beginning = \[T_4 = T_{3 + 1}\]
\[\therefore T_4 =^{9}{}{C}_3 \left( x^{9 - 3} \right) \left( \frac{2}{x} \right)^3 \]
\[ = \frac{9 \times 8 \times 7}{3 \times 2}\left( x^6 \right)\left( \frac{8}{x^3} \right)\]
\[ = 672 x^3\]
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