# Thread: Summation of square root

1. ## Summation of square root

Hi all,

I need a little help with this summation problem.

Find the value of,

$\displaystyle \sum_{r=1}^4 a_r$

For, $\displaystyle a_r = 2 + \sqrt r$

I tried to solve it like this,

$\displaystyle = 2(4) + \sum_{r=1}^4 \sqrt r$

What is the series,

$\displaystyle 1, \sqrt 2, \sqrt 3, \sqrt 4, + ...$.

Its clearly not a A.P. It also doesn't seem like a G.P. How do I calculate the sum of such a series?

P.S. Latex doesn't work anymore. I used QuickLatex to explain the problem.

2. Isn't it just ?

3. @Prove It, Thanks for your reply. I realize the no. of terms are small. But I want to learn how to do the summation of square root bit, when I am faced with a similar problem with a larger upper limit

4. In short, you can't. When all else fails, write each term and simplify.

5. Originally Posted by Prove It
In short, you can't.
Hah! Prove It! Sorry couldn't resist. Thanks.

6. Originally Posted by Prove It
Isn't it just ?
Yes it is.