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Simple, but fun

  1. Mar 2, 2006 #1
    Can you count and add all the numbers 1-100 without using a calculator?
     
  2. jcsd
  3. Mar 2, 2006 #2
    You got me!
     
  4. Mar 2, 2006 #3

    VietDao29

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    As a metter of fact, I think I can :wink:
    If I am not mistaken then Gauss did it centuries ago...
     
  5. Mar 2, 2006 #4
    Let's hope not! ... Maybe all the *integers*, tho :)
    (And yeah, you can use the old ((S+F)/2)*(F-S+1) trick to add all the integers between S and F)

    DaveE
     
  6. Mar 2, 2006 #5
    Well it wasn't easy, but there are 100 of them.
     
  7. Mar 2, 2006 #6
    Yes sir, an old wive's tale is that he one day was punished in 3rd grade class and the teacher asked him to add all the numbers 1-100 thinking it would keep him busy, but he was able to reply the answer back to her in a matter of seconds.
     
  8. Mar 3, 2006 #7
    yea u just use the formula...sum = 0.5n(n+1)

    so 0.5 x 100 x 101 =50 x 101 = 5050
     
  9. Mar 3, 2006 #8

    AKG

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    Yes, 1 + ... + 100 = (1 + 100) + (2 + 99) + ... (50 + 51) = (101) + (101) + ... + (101) [50 times] = 50 x 101 = 5050. I heard that this is how Gauss did it.
     
  10. Mar 16, 2006 #9
    So what you're all saying is, find the average value (50.5) and mutiply by the number of terms.
     
  11. Mar 16, 2006 #10
    What is 50.5 the average value of?
     
  12. Mar 17, 2006 #11

    VietDao29

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    I think he meant the average value of the first term and the last term, ie:
    (1 + 100) / 2 = 50.5
     
  13. Mar 17, 2006 #12
    50.5 is the average value of all the numbers 1 to 100 inclusive.

    If there were an odd number of terms in an evenly spaced sequence the average would be the middle term.
    As this sequence is even the average value is the average of the two middle terms - 50 & 51.
     
  14. Mar 17, 2006 #13
    Ahh, I must have misread something.
     
  15. Mar 17, 2006 #14
    Not so much misread as partially read. 50.5 is not only the average of 1 and 100. It is also the average of 2 and 99, 3 and 98, etc. That is, it is the average of the set of integers from 1 to 100.
     
  16. Mar 27, 2006 #15
    im lost....
     
  17. Mar 27, 2006 #16

    Mk

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