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Ok, I hope somebody has a really good logical explanation of this, or maybe even some other awesome examples?

• pja 13y ago
  The fact that 10000 - 2 = 9998 probably has something to do with it. Compare and contrast the result for 1 / 99998.
  • archgoon 13y ago
    Pretty much. 1/9998 = 1/(10000-2) = 1/(10000)*1/(1-2/(10000) Since 2/10000 is very small, it is well approximated by the taylor expansion for 1/(1-x), which is simply Sum(x^n) Since x is 2/10000, we get powers of two, which keep getting shifted to the right. Like a bit pattern, they don't overlap when added, so we get the sequence above.
• fjcaetano 13y ago
  Sorcery!
  • camus2 13y ago
    math voodoo ! it's beautifull indeed.
• elektronaut 13y ago
  Similarily, 1/9999 gives you powers of 1 (which is just 1), 1/9997 powers of 3, and so on.
• cangencer 13y ago
  A mathematical explanation: http://calculus7.org/2012/02/25/playing-with-numbers-998001-explained/ http://calculus7.org/2012/02/25/playing-with-numbers-998001-...
• impendia 13y ago
  1/(1 - x) = 1 + x + x^2 + x^3 + x^4 + ... so, 1/(1 - .0002) = 1 + .0002 + .0002^2 + ... and 1/9998 = .0001/(1 - .0002).
• ronaldx 13y ago
  Explanation: 0.0001+0.00000002+0.00000000004 etc = 2^0/10^4 + 2/10^8 + 2^2/10^12 etc which is a geometric sequence with common ratio 2/10000 and first term 1/10000 So it has an infinite sum of (1/10000)/(9998/10000) = 1/9998 Same for powers of 3: 1/9997 Actually 1/8 = 0.125 is an example of this; it just breaks down very early because 4+0.8+0.16+0.032+0.0064+... = 5
• deleted 13y ago
  [deleted]
• nanofortnight 13y ago
  Simple high-school maths. S = 0.00010002000400080016... S = 0.0001 + 0.0000 0002 + 0.0000 0000 0004 + 0.0000 0000 0000 0008 + ... S = 2^0 / 10000^0 + 2^1 / 10000^1 + 2^2 / 10000^2 + 2^3 / 10000^3 + ... S = sum to infinity of (2/10000)^i You might have noticed this is a geometric series with ratio 2/10000 = 0.0002. S = 0.0001 / (1 - 0.0002) = 0.0001 / 0.9998 = 1/9998