# Adding series of fractions in an equation.

#### Submerged

Hey, I'm looking for some help creating an equation. It's possible that this isn't really possible, but I figure there are more clever people than I in here that could use a puzzle . I know this could be done using calculus symbols, but this is for a PHP script so I am looking for a more efficient (and, if luck permits, simpler) equation.

Basically, I'm trying to add up the sum of 1 divided by every number between X an Y.
For instance, if X = 5 and Y = 10, this would add (1/5+1/6+1/7+1/8+1/9+1/10). I could simply make a recursive function, but if there is a simple way to do this it would be a lot more efficient (as the X and Y could theoretically get up in the thousands).

Is there a simple way to find this (preferable in a normal y = ?x kind of equation -- though logs, exponents and other things like that are fine)?

Thanks!
- Submerged

P.S. If this belongs in a different thread, I'm sorry . This could be answered via calc, but I figured looking for a simpler answer meant going to a simpler forum.

#### dwsmith

MHF Hall of Honor
Hey, I'm looking for some help creating an equation. It's possible that this isn't really possible, but I figure there are more clever people than I in here that could use a puzzle . I know this could be done using calculus symbols, but this is for a PHP script so I am looking for a more efficient (and, if luck permits, simpler) equation.

Basically, I'm trying to add up the sum of 1 divided by every number between X an Y.
For instance, if X = 5 and Y = 10, this would add (1/5+1/6+1/7+1/8+1/9+1/10). I could simply make a recursive function, but if there is a simple way to do this it would be a lot more efficient (as the X and Y could theoretically get up in the thousands).

Is there a simple way to find this (preferable in a normal y = ?x kind of equation -- though logs, exponents and other things like that are fine)?

Thanks!
- Submerged

P.S. If this belongs in a different thread, I'm sorry . This could be answered via calc, but I figured looking for a simpler answer meant going to a simpler forum.
$$\displaystyle \sum_{n=1}^6\frac{1}{n+4}$$

#### Submerged

Thanks for the help, dwsmith, but is there anyway to do it without using calculus like that (i.e., a recursive summation)? I'm working with a PHP script on it, so I'm trying find a simpler equation (a y = ???x kind of deal) that would be more efficient for that code .

#### dwsmith

MHF Hall of Honor
Thanks for the help, dwsmith, but is there anyway to do it without using calculus like that (i.e., a recursive summation)? I'm working with a PHP script on it, so I'm trying find a simpler equation (a y = ???x kind of deal) that would be more efficient for that code .
PHP?

#### Submerged

If you're asking what PHP is (hard to tell with just the question mark ), it's a web programming language. It can do all the basic math functions (exponents, logs, etc.), and I can easily do what I'm trying here by calling a recursive that will simply do each part (1/2, 1/3, etc.) and then add them together, but that would be inefficent.

#### undefined

MHF Hall of Honor
Hey, I'm looking for some help creating an equation. It's possible that this isn't really possible, but I figure there are more clever people than I in here that could use a puzzle . I know this could be done using calculus symbols, but this is for a PHP script so I am looking for a more efficient (and, if luck permits, simpler) equation.

Basically, I'm trying to add up the sum of 1 divided by every number between X an Y.
For instance, if X = 5 and Y = 10, this would add (1/5+1/6+1/7+1/8+1/9+1/10). I could simply make a recursive function, but if there is a simple way to do this it would be a lot more efficient (as the X and Y could theoretically get up in the thousands).

Is there a simple way to find this (preferable in a normal y = ?x kind of equation -- though logs, exponents and other things like that are fine)?

Thanks!
- Submerged

P.S. If this belongs in a different thread, I'm sorry . This could be answered via calc, but I figured looking for a simpler answer meant going to a simpler forum.
Why would you use a recursive function when a simple loop would do?

PHP:
<?php
$y = 10;$sum = 0;
for ($x = 5;$x <= $y;$x++)
$sum += 1/$x;
echo \$sum;
?>
As for whether there is a simple formula you could use, I don't know.

But how efficient do you need to be? Even with thousands of iterations, the above loop will execute in very little time.

By the way $$\displaystyle \sum$$ is not a calculus symbol. No need to be afraid of it, it just means take the sum.

#### Submerged

True, I supposed a loop doesn't count as a recursive function . If PHP can do it that quickly, then I can just leave it as it is -- I'm not as familiar with the power behind a server as most, all I know is how to write code.

#### undefined

MHF Hall of Honor
True, I supposed a loop doesn't count as a recursive function . If PHP can do it that quickly, then I can just leave it as it is -- I'm not as familiar with the power behind a server as most, all I know is how to write code.
Yeah well 1 GHz means 1 billion cycles per second... there's a lot that can be done with speeds measured in GHz.