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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.
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 left-endpoint and right-endpoint
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, AP-Calculus, 19 May 2006
http://mathforum.org/kb/thread.jspa?messageID=4725124

Dave L. Renfro
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