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Hi,
Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this?
[itex]\sum^{n}_{i=1}\sqrt{f(i)}[/itex]
The specific case is given with constant c:
[itex]\sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1}[/itex]
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?
[itex]\sum^{n}_{i=1}c^4i^4+\sum^{n}_{i=1}c^2i^2+\sum^{n}_{i=1}1[/itex]
[itex]=c^4\sum^{n}_{i=1}i^4+c^2\sum^{n}_{i=1}i^2+\sum^{n}_{i=1}1[/itex]
Thanks!
Is there a general algebraic expression for the sum of a function inside a radical? I mean for something like this?
[itex]\sum^{n}_{i=1}\sqrt{f(i)}[/itex]
The specific case is given with constant c:
[itex]\sum^{n}_{i=1}\sqrt{c^4i^4+c^2i^2+1}[/itex]
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?
[itex]\sum^{n}_{i=1}c^4i^4+\sum^{n}_{i=1}c^2i^2+\sum^{n}_{i=1}1[/itex]
[itex]=c^4\sum^{n}_{i=1}i^4+c^2\sum^{n}_{i=1}i^2+\sum^{n}_{i=1}1[/itex]
Thanks!