Originally Posted by

**Furyan** Hello,

The question is:

In the binomial expansion of $\displaystyle (2k + x)^n$, where *k *is a constant and *n *is a positive integer, the coefficient of $\displaystyle x^2$ is equal to the coefficient of $\displaystyle x^3$. Prove that *n* = 6*k* + 2.

I got as far as:

$\displaystyle ^{n}C_{2}(2k)^{n - 2} = $$\displaystyle ^{n}C_{3}(2k)^{n - 3}$

I tried simplifying and got:

$\displaystyle ^{n}C_{2}= $$\displaystyle ^{n}C_{3}(2k)^{-1}$

I then tried simplifying the factorials, but couldn't see how I was going to end up with the required result.

Some help would be very appreciated.

Thank you.