I have a question about the negative binomial process.

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

Now I have to show that

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

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

Plz Help