Question

Find the middle term in the expantion of (1-3x+3x^2-x^3)^2n

Answer 1

since the power is 2n so the total terms is (2n+1)

so middle term is (2n + 1)/2

so (x³ - 3x² +3x - 1)$^{2n}$

⇒ (x-1)$^{6n}$

so total terms is 6n + 1

so middle term is (6n + 1 + 1)/2 = 3n + 1

so $T_{3n+1}=^{6n}C_{3n}x^{3n}*-1^{3n}$

= $- \frac{6n!}{3n!3n!}x^{3n}$  is n is odd

else 

$\frac{6n!}{3n!3n!}x^{3n}$ if n is even