>>29
I'm not
>>28, but I'd try it this way:
Let z_n be a series of integers and s_n its sequence of partial sums.
Assuming z_n was convergent, it must also pass the cauchy test, which delivers for n > N(epsilon) with epsilon < 1:
|s_n - s_(n+1)| = z_(n+1) < 1, but the only number in the integers < 1 is 0.
So that means we only have a finite amount of numbers > 0 in a convergent series of integers and with that knowledge we can resort to the closure of integers under addition.
q.e.d.