Floor((n+1)/2)^2 - floor(n/2)^2 - 1/2(1-(-1)^n)(n)=0

It works for every n and I can simplify it down here and there but can’t seem to get near the answer.

The floor functions keep restricting me.

I can get floor out by adding variables in but this gives me more to work with and doesn’t seem to cancel down. E.g (((n+1)/2)+a)^2 - ((n/2)+b)^2

I could separate it for n=even and n=odd, but surely if this is true for all values of n then it can be rearranged.

Help would be greatly appreciated

Thanks.

It works for every n and I can simplify it down here and there but can’t seem to get near the answer.

The floor functions keep restricting me.

I can get floor out by adding variables in but this gives me more to work with and doesn’t seem to cancel down. E.g (((n+1)/2)+a)^2 - ((n/2)+b)^2

I could separate it for n=even and n=odd, but surely if this is true for all values of n then it can be rearranged.

Help would be greatly appreciated

Thanks.

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