1.
I guess you don't know Newton's generalized binomial theorem...
I considered a multiple of k.
So:
2.
So:
Hey guys I need help with this question
and the answer given in the solution to the question is that since
I know by substituting in values for n in that they all appear divisible by 3, is this a definite rule, is there a proof of this without using induction?
The same goes for , how do we know that this is divisble by 2 for all values of n without induction
If we can't use induction to prove those divisbility by 3 and 2, then isn't the question kinda invalid?
Thanks
The is easy, without any tricks like below. is an odd number, so subtracting 1 from it gives us an even number.
is a bit trickier. Note that when we expand by the binomial theorem:
of which you can prove (using the combinatorial coefficients) that every coefficient is divisible by 3.
-Dan