Prove by induction that (binomial theorem)
$$
\binom{s}{s} + \binom{s+1}{s} + \dotsb + \binom{n}{s} = \binom{n+1}{s+1}
$$
for all $s$ and all $n>s$.

I used base case $s=0$, and I got my base case to work. However when I go to my induction step, I can’t seem to get it to work.