Show that, for n > 0,
I know i am supposed to use the binomial theorem which is just,
I am really just not sure where to start though
Thank you for any help/tips
(if this needs to be moved to Discrete Mathematics, Set Theory and Logic, would a mod please move it. thank you)
Ok great i think i got it.
for a = 1 and b = -1 and using any number where n > 0 you can see that when plugged into the binomial theorem it is a repeating pattern of (in this case) 2 + -2 + 2 + -2 .... which therefore will = 0 proving to be true.
Does this seem correct or am i missing something? I am very new to proofs (this is actually my first one haha )
What would the values be ?
and "yes", you are missing something, not only that n could be even giving an odd number of terms,
so the sum would not be zero.
TheCoffeeMachine and Plato are drawing your attention to the fact that
The expansion is
I have been looking over these posts again for the past day or so and I still can't seem to wrap my mind around this.
I get using A = -1 and B = 1 and using the binomial theorem will give you the expansion
I guess i just dont get how this proves that for n > 0
I feel like i am making this much more difficult than it should be
You said you are supposed to use the binomial theorem. So for we have,
let a = -1 and b = 1. This equality then becomes,
So the binomial theorem actually proves it for you. You just need to plug in those values. This is just a special case of the binomial theorem.
You could also use the binomial theorem to show that
in each case you are using the special cases of a theorem that has already been proven for you. I hope that helps you out a bit.