Well actually we dont know!. This might surprise you a bit but the actual fact is that from centuries mathematicians have debated over this . It was scientist Srinivasa Ramanujan who had proved the fact that sum of all postive numbers is actually very small and by small I mean just -1/12.
If you dont believe me then take a look at the above snapshot taken from Wikipedia. If you are more interested(Which you should be!!) , then you can go to this link ! http://en.wikipedia.org/wiki/1%2B2%2B3%2B4%2B%E2%8B%AF