# Sum of function inside radicals

1. Oct 24, 2012

### hddd123456789

Hi,

Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this?

$\sum^{n}_{i=1}\sqrt{f(i)}$

The specific case is given with constant c:

$\sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1}$

And I supposed a related question is that, is there some way of extracting out just the radical as a separate sum of sqrt(i) or something which will leave three relatively simpler sums below?

$\sum^{n}_{i=1}c^4i^4+\sum^{n}_{i=1}c^2i^2+\sum^{n}_{i=1}1$
$=c^4\sum^{n}_{i=1}i^4+c^2\sum^{n}_{i=1}i^2+\sum^{n}_{i=1}1$

Thanks!

2. Oct 24, 2012

### HallsofIvy

No, that cannot be simplified.

3. Oct 24, 2012

### hddd123456789

:(

Is there any chance a novice could perhaps determine a pattern to the series given enough time and energy? Or is there some strong mathematical reason why it simply isn't possible?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook