## neg. process

I have a question about the negative binomial process.

It is given that $\left(X_{k}\right)_{k=1,2,3,.....}$ is a sequence of geometric random variables
And $S_{k}=X_{1}+.....+X_{k}$ is negative binomial (i,p)
So $\ P\left(S_{i}=k\right)$ a negative binomial distribution (i,p)

Now I have to show that

$P\left(S_{i}\leq k , S_{i+1}=k+n\right)$ =
$P\left(S_{i+1}=k+1\right)$ $\left(1-p\right)^{n-1}$

But I don't know well how to work out the joint distribution

Plz Help