Question

The 5^th term from the end in the expansion of $\left( \frac{x^{3}}{2} - \frac{2}{x^{3}} \right)^{9}$ is

• A. $63x^{3}$
• B. $- \frac{252}{x^{3}}$
• C. $\frac{672}{x^{18}}$
• D. None of these

Answer 1

Answer: (B)

$- \frac{252}{x^{3}}$

Answer 2

5^th term from the end = $(9 - 5 + 2)^{th}$ term from the beginning in the expansion of $\left( \frac{x^{3}}{2} - \frac{2}{x^{3}} \right)^{9}$= $T_{6}$

⇒ $T _ { 6 } =$ $T_{5 + 1} =^{9} ⥂ C_{5}\left( \frac{x^{3}}{2} \right)^{4}\left( - \frac{2}{x^{3}} \right)^{5} = -^{9} ⥂ C_{4}.2.\frac{1}{x^{3}} = - \frac{252}{x^{3}}$.