Mass function; negative binomial distribution

Question

I want to proof that the mass function of the negative binomial distribution satisfies that it adds up to 1 if we take all x in R.

My textbook starts as follows: enter image description here

I don't understand how they substituted l in (k-1) choose (n-1). I would have done the following: enter image description here - but this way I don't get their result.

Could someone help me with this?

(I am new here, so I'm not allowed to post pictures yet. That's why I'm posting links instead of pictures).

Answer 1

Binomial coefficients are symmetric. \begin{eqnarray*} \binom{ k-1}{ n-1}=\binom{ k-1}{ k-n} \end{eqnarray*} Does this help ? Sha, Highlight the above equation & right click, then choose the option show math as & then TeX command ... it will show you the tex commands to write equations.