i just saw a proof in which you calculate the sum of all natural numbers and get to an astonishing -1/12! a negative number! i just cant get a good grip on that...its hard to make sense of it. the proof involves: S1= 1-1+1-1..... S2= 1-2+3-4+5.... S3= 1+2+3+4+5.... he goes on to prove that S1 = 1/2 (the average of the 2 possibilities) S1 = 2 S2 and therefore S2 equals 1/4 S3 - S2 = 4S3 from this, -S2 = 3S3 since S2 is already 1/4, the sum of all natural numbers, S3, becomes -1/12 this is the weirdest thing i have ever seen. please help me make sense of it.
