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karthik science forum beginner
Joined: 28 Jun 2006
Posts: 2

Posted: Wed Jun 28, 2006 5:09 pm Post subject:
sequence sum



Hi friends,
can anyone plz help me out in solving this problem.
The problem goes something like this.
Derive a formula to find the sum of the following series.
sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+            +sqrt(n) where
n>=1
regards,
karthik. 

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Dave L. Renfro science forum Guru
Joined: 29 Apr 2005
Posts: 570

Posted: Wed Jun 28, 2006 6:11 pm Post subject:
Re: sequence sum



karthik wrote:
Quote:  can anyone plz help me out in solving this problem.
The problem goes something like this.
Derive a formula to find the sum of the following series.
sqrt(1)+sqrt(2)+sqrt(3)+sqrt(4)+            +sqrt(n)
where n>=1

I don't think there's a simple closed form expression for
this sum, but you can use leftendpoint and rightendpoint
Riemann sums for y = sqrt(x) with delta(x) = 1 on the
interval [0,n] to see that a rough estimate for the
sum is n^(3/2). For slightly more details on this,
see my post at
The Math Forum, APCalculus, 19 May 2006
http://mathforum.org/kb/thread.jspa?messageID=4725124
Dave L. Renfro 

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