Eggs drops and super eggs drop pure math solutions

Eggs drops and super eggs drop pure math solutions
in this video, I mathematically try to prove the solution of eggs drop for
k eggs drops.
Basically, I solved the following:
Super Egg Drop
Egg Drop With 2 Eggs and N Floors

0:00 start
1:00 one egg drop
4:00 Egg Drop With 2 Eggs and N Floors
13:00 Egg Drop With 3 Eggs and N Floors
24:00 Super eggs drop with k eggs
25:00 prove the formula by mathematical induction
32:07 prove the lemma

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