The question is:
In the binomial expansion of , where k is a constant and n is a positive integer, the coefficient of is equal to the coefficient of . Prove that n = 6k + 2.
I got as far as:
I tried simplifying and got:
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.
Hello Prove It,
Wow! Thank you so much, that's totally brilliant. I didn't anticipate such a comprehensive reply. I see that by dividing by , instead, you avoided getting . Why didn't I think of that? As for what you did to simplify the factorials, I'm going to have to work through it slowly to make sure I understand what you have done.
Thank you again. I really appreciate your efforts.