My friend shared a link in facebook, which is a proof to the statement that the summation of natural numbers is -1/12. http://www.youtube.com/watch?v=w-I6XTVZXww is the link explaining the proof. It is weird and counter intuitive. For those who does not want to spent 8 minutes watching the video, the proof is the following. If you have watched the video you can skip the proof (I have made a slight modification in summing up Grandi’s series, though.)
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| From Necker cubicle |
This is madness.. More such tweaks and you will end up showing 1 = 2. A silly attempt in that direction is the next derivation.
If S = -1/12
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| From Necker cubicle |
PS1: Correct me!
PS2: On a different note, did you know that 0.99999…. = 1 ?
1. Nothing to correct. In the new world order, 9 is the new 12.
Anyway, when I was sent that video, I responded with this:
Sum of first n integers, is 1/2 * n * (n + 1). What the/you’re looking for is the limit of it as n -> infinity. That is:
http://www.wolframalpha.com/input/?i=lim+n-%3Einfinity+1%2F2+n+%281%2Bn%29
2. Yes, I did. (that’s a cute little proof though).
so, 9 = 12 = infinity ..