Hello Ian

Welcome to Math Help Forum! Originally Posted by

**Cowan5** Hi I have a problem regarding summation and the index numbers. It is from a formula used in the betting industry.

"Consider a race with **n** runners with starting prices (the odds of each horse) denoted by **Si:1** such that there are **ni** **(>0)** horses at **Si (i=1,2,3...,k)** with **S1**<**S2**....**Sk**."

Let **p ****= Σ ni/(1+Si)**

I want to find **p** but I don't understand the terms **ni **and** Si**, help appreciated.

Regards,

Ian

Let me unpack this for you:
there are

**ni** **(>0)** horses at

**Si (i=1,2,3...,k)** with

**S1**<

**S2**....

**Sk**.

means there are:$\displaystyle n_1$ horses at odds of $\displaystyle S_1:1$

$\displaystyle n_2$ horses at odds of $\displaystyle S_2:1$

...

$\displaystyle n_k$ horses at odds of $\displaystyle S_k:1$

and the numbers $\displaystyle S_1, S_2, ..., S_k$ are in ascending order of size: $\displaystyle S_1<S_2<...<S_k$.

Then the formula $\displaystyle p = \sum_{i=1}^k\left(\frac{n_i}{1+S_i}\right)$ means that:

$\displaystyle p = \frac{n_1}{1+S_1}+\frac{n_2}{1+S_2}+...+\frac{n_k} {1+S_k}$

Does that make it clearer?

Grandad