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Oh Mighty Calculator

  1. May 31, 2009 #1
    like many people have done with their calculators, I was dividing 987654321 by 123456789. and I realized...

    sum(0 to N) 987654321 * 10^(N*j)
    divided by
    sum(0 to N) 123456789 * 10^(N*j)

    where N can be any positive integer and j is in the real domain, there is a constant.


    Am I weird and stupid?
     
  2. jcsd
  3. May 31, 2009 #2

    CRGreathouse

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    sum(0 to N) 987654321 * 10^(N*j) = 987654321 * sum(0 to N) 10^(N*j)
    sum(0 to N) 123456789 * 10^(N*j) = 123456789 * sum(0 to N) 10^(N*j)
    so their quotient is indeed constant.

    I ended up not needing this: For N a positive integer, sum (j=0,N,10^(N*j)) = (10^(N^2+N)-1)/(10^N - 1).
     
  4. Jun 2, 2009 #3
    omg omg I'm like so stup.

    something times (thing/thing) = something.

    how can I be so stupid...
     
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