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Sum of the square root of integers from 1 to n

  1. Jan 30, 2008 #1
    1. The problem statement, all variables and given/known data
    I want to know whats the formula to calculate the sum of the square root of integers from 1 to n.
    I got an identity from wikipedia but its too complicated for me, it involves bernoulli's number, i don't know what is that.

    2. Relevant equations

    3. The attempt at a solution
    In excel i managed to get a power regression and i got the formula 0.701n^(1.492), its kind of accurate but not 100%.

    I hope someone could help me.
  2. jcsd
  3. Jan 30, 2008 #2


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    Science Advisor
    Homework Helper

    Bernoulli numbers

    The Wikipedia page entitled "Bernoulli number" has the definition:
  4. Jan 30, 2008 #3

    D H

    Staff: Mentor

    Exactly what Bernoulli numbers are (but see EnumaElish's post) is a bit irrelevant here because that identity, known as Faulhaber's formula, is only valid for integer powers.

    What you want is something more general. See the mathworld article on power sums, link here, particularly equations 10 through 12.
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