The sum of all positive integers

Student PIRGs, Jan 17, 2014
Commentary by Stephen Downes
files/images/infinity.JPG

Today's most interesting bit of information: if you take the sum of an infinite set of numbers, what do you get? In other words, [1 + 2 + 3 + 4 + 5 + ... infinity] = ? The answer? -1/12. How can this be, you ask? It's because it goes to infinity, which means there's never a definite sum. For example, take this sequence: [1 - 1 + 1 -1 + 1 ...] = ? What it equals depends on where you stop. It would either be 1 or 0. But, since you never stop, it can't be either, so we take the value of this sequence to be an average, 1/2. The same sort of logic is at work with the first sequence. Watch the video for a full explanation. (You know what would also make sense using this logic? 42. Conclusion? Life, the universe and everything is infinite.)

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