Formula for sqrt of i in limit summations?

[ucdawg12]

I can't seem to find if there is an equation for the sqrt of i or not, i know that the formula for i is (n(n+1))/2 and for i^2 its (n(n+1)(2n+1))/6, but I can't find an formula for the sqrt of i


thanks

 

[cyby]

I don't recall there being one.

Mathematica outputs it as:

HarmonicNumber[k, -1/2]

For an input of Sum[n=1..k] Sqrt[n]

http://mathworld.wolfram.com/HarmonicNumber.html is the corresponding mathworld link..

 

[quantumdude]

I can't seem to find if there is an equation for the sqrt of i or not, i know that the formula for i is (n(n+1))/2 and for i^2 its (n(n+1)(2n+1))/6, but I can't find an formula for the sqrt of i

There isn't one that I know of. Let me ask you something: Are you trying to do a Riemann sum for a function such as f(x)=x^1/2? If so, then you might be better off using subintervals of variable width, such that the point x=c_i that you use in the ith subinterval depends on i². Then you can use your nifty little formulas.