12.5.3 Can you answer these questions?

12.5.3.1 Mathematica does not evaluate $\sum_ m=0 ^n\binom mi n-m\choose k-i = n+1\choose k+1 $
12.5.3.1 Mathematica does not evaluate $\sum_ m=0 ^n\binom mi n-m\choose k-i = n+1\choose k+1 $

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=318558

I recently saw q3964942, in which the asker asserted the titled identity 
$$\sum_{m=0}^n\binom mi{n-m\choose k-i}={n+1\choose k+1}$$ 
to which angryavian had commented on 2020-12-28 
 
Shouldn't your ... 
[summation]
 
asked by DroneBetter https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=111614 Score of 2