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![]()