- #1
hddd123456789
- 92
- 0
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!
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!
