Hi,

I'm required to show that

$\displaystyle {n \choose r} + 2{n \choose r-1} + {n \choose r-2} = {n+1 \choose r}$

Now I know that $\displaystyle {n \choose r} + {n \choose r-1} = {n+1 \choose r}$

and we can write the LHS as

$\displaystyle \left[{n \choose r} + {n \choose r-1}\right] + {n \choose r-1} + {n \choose r-2}$

$\displaystyle ={n+1 \choose r} + {n \choose r-1} + {n \choose r-2}$

Which means for the equality to hold I would have to show that $\displaystyle {n \choose r-1} + {n \choose r-2} = 0$, which I don't think is right.

So where have I messed up?

Thanks