I see your point. There are indeed a couple of errors in there. But the point still holds. The sign is wrong on the sum of the left hand side. And a (-1)^(a+1)

I see your point. There are indeed a couple of errors in there. But the point still holds. The sign is wrong on the sum of the left hand side. And a (-1)^(a+1) is missing on the RHS. But these do not change the "this is an integer" claim. Further down, it does assume that 'a' is even, without saying so . But if 'a' was odd, things would still be the same but we would have a ]-1,0[ interval. Anyway, I'm not a mathematician so I'm probably missing stuff.