Q. The $r$th terms in the expansion of $(a + 2n)^{n}$ is
A) $\frac{n(n + 1)\ldots(n - r + 1)}{r!}a^{n - r + 1}(2x)^{r}$
B) $\frac{n(n - 1)\ldots(n - r + 2)}{(r - 1)!}a^{n - r + 1}{(2x)}^{r - 1}$
C) $\frac{n(n + 1)\ldots(n - r)}{r + 1}a^{n - r}{(x)}^{r}$
D) None of the above
Explanation
(b)
The $r$th term of $(a + 2n)^{n}$ is $\ ^{n}C_{r - 1}{(a)}^{n - r + 1}{(2x)}^{r - 1}$
$= \frac{n!}{(n - r + 1)!(r - 1)!}a^{n - r + 1}(2x)^{r - 1}$
$= \frac{n(n - 1)\ldots(n - r + 2)}{(r - 1)!}a^{n - r + 1}{(2x)}^{r - 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.