Sum of the square root of integers from 1 to n

[Thirit]

Homework Statement

I want to know what's 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.

Homework Equations

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.
Thanks

 

[EnumaElish]

Bernoulli numbers

The Wikipedia page entitled "Bernoulli number" has the definition:

Bernoulli numbers may be calculated by using the following recursive formula:
[tex]\sum_{j=0}^m\left(\begin{array}{ c }
m+1 \\
j
\end{array}\right)B_j=0[/tex]
for m > 0, and B₀ = 1.

 

[D H]

[I want to know what's 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.

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, http://mathworld.wolfram.com/PowerSum.html" , particularly equations 10 through 12.