Hi,(adsbygoogle = window.adsbygoogle || []).push({});

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!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sum of function inside radicals

Loading...

Similar Threads - function inside radicals | Date |
---|---|

I Trying to get an explicit function(ish) | Yesterday at 5:39 PM |

B Beginner function question | Feb 17, 2018 |

I Correct notation for some functional expressions | Feb 17, 2018 |

I Question about the Divisor Function/Sums and Project Euler | Feb 16, 2018 |

I Putting a point inside a triangle in 3D space | Dec 7, 2017 |

**Physics Forums - The Fusion of Science and Community**