Question

If A and B are the coefficient of $x^{n}$ in the expansions of $(1 + x)^{2n}$ and $(1 + x)^{2n - 1}$ respectively, then

• A. $A = B$
• B. $A = 2B$
• C. $2A = B$
• D. None

Answer 1

Answer: (B)

$A = 2B$

Answer 2

$A =$coefficient of $x^{n}$ in $(1 + x)^{2n}$ = $2n ⥂ C_{n} = \frac{(2n)!}{n!n!}$

= $\frac{2.(2n - 1)!}{(n - 1)!n!}$.....(i)

$B =$ coefficient of $x^{n}$ in $(1 + x)^{2n - 1} ⥂ =^{2n - 1}C_{n} = \frac{(2n - 1)!}{n!(n - 1)!}$.....(ii)

By (i) and (ii) we get, $A = 2B$`