Question

I should know this. It's a real problem from "out in the wild" but I've long forgotten how to do real math :(

I need to simplify (not solve) the following equation:

α/13 + α/14 + α/15 + α/16 + α/17 … α/48

In case you were wondering, there are 36 items in this little gem.

I am certain there is some elegant way to show this such as { (n x α) ÷ [(13+48)÷2]}n where n = the number of items …. But I don’t have three days derive the equation myself.

Answer 1

\[\large \frac{\alpha}{13}+\frac{\alpha}{14}+\frac{\alpha}{15}+...+\frac{\alpha}{48} \qquad \rightarrow \qquad \alpha\left[\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+...+\frac{1}{48}\right]\]


Which should simplify to something really nice like this,
\[\huge \alpha\left[\sum_{i=13}^{48}\frac{1}{i}\right]\]

Beyond that, Hmmmm I'm trying to remember :) heh

Answer 2

Thank you. Correct me if I'm wrong, but I think the lovely picture you've drawn (with Sigma) is more of a description than a formula, is that correct? Gads, it's been years. If anyone in this forum is wondering who actually uses this stuff, I guess I"m living proof that it does come up (although not daily to keep it fresh).

Answer 3

Ummmm I suppose that's prolly true :) It's like a really compact way of expressing a large set of terms.

But it certainly is a real device, used in programming and other stuff.
Yah there might be a nice way to actually combine all the fractions, but I'm not quite seeing it right now. And Wolfram isn't being very helpful, grr!

Answer 4

Thank you Zepdrix! It's a great forum. I'm glad there are people out there willing to share their knowledge.