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## Homework Statement

Prove that

[tex] \sum^{l}_{k=0} [/tex] [tex] n \choose k [/tex] [tex] m \choose l-k [/tex] = [tex] n+m \choose l [/tex]

Hint: Apply the binomial theorem to (1+x)

^{n}(1+x)

^{m}

## Homework Equations

## The Attempt at a Solution

I apply the hint to that thing to get [tex] \sum^{n}_{j=0}[/tex] [tex] n \choose j [/tex] [tex]x^j \sum^{m}_{k=0}[/tex] [tex] m \choose k [/tex] [tex]x^k [/tex]

= [tex]\sum^{n}_{j=0}\sum^{m}_{k=0}[/tex][tex]n\choose j[/tex][tex]m\choose k[/tex][tex]x^{j+k} = \sum^{n+m}_{l=0}[/tex][tex]n+m \choose l[/tex][tex]x^l [/tex]

Now I am stuck.