$$r$$ and $$n$$ are positive integers $$\,r > 1,\,n > 2$$ and coefficient of $$\,{\left( {r + 2} \right)^{th}}$$ term and $$3{r^{th}}$$ term in the expansion of $${\left( {1 + x} \right)^{2n}}$$ are equal, then $$n$$ equals
A
$$3r$$
B
$$3r + 1$$
C
$$2r$$
D
$$2r + 1$$
Explanation
$$\,{\left( {r + 2} \right)^{th}}$$ term = $${}^{2n}{C_{r+1}}{\left( x \right)^r}$$
And coefficient of $$\,{\left( {r + 2} \right)^{th}}$$ = $${}^{2n}{C_{r+1}}$$
$$3{r^{th}}$$ term = $${}^{2n}{C_{3r - 1}}{\left( x \right)^{3r - 1}}$$
And coefficient of $$3{r^{th}}$$ term = $${}^{2n}{C_{3r - 1}}$$
According to the question,
$${}^{2n}{C_{r+1}}$$ = $${}^{2n}{C_{3r - 1}}$$