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Number of terms in a series

  1. Aug 4, 2004 #1
    How many terms would I need in the sum:
    3 + 12 + 27 + 48 + .....

    ( 1x + 4x + 9x +16x + ...)

    to get close to the number 10^57 ?
     
  2. jcsd
  3. Aug 4, 2004 #2

    Hurkyl

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    Use the sum of squares formula.

    1^2 + 2^2 + ... + n^2 = n (n+1) (2n+1) / 6
     
  4. Aug 5, 2004 #3

    arildno

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    Actually, if you allow an error margin of 10^58, one term is enough!!
    Since most numbers are larger than 10^58, 3 is a pretty close approximation to 10^57..
     
  5. Aug 5, 2004 #4
    Thanks for helping.
     
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