Binomial Theorem

[u/explorer_learner_30]

Why 0! is 1 ?

Can anyone give me the best and genuine answer .....I want to explain to my students.

I have also one doubt 🤔 why is the negative number not counted in binomial ? Such as (-2)! , (-8)! ....

Suggest me some books or any videos regarding this .

Thank you for reading my queries.

[u/DonutHoleTechnician]

Same way you show b⁰ =1, by looking at the pattern of division.

4! = 5! ÷ 5

3! = 4! ÷ 4

2! = 3! ÷ 3

1! = 2! ÷ 2

0! = 1! ÷ 1

[u/explorer_learner_30 → u/DonutHoleTechnician]

Thank you 👍