Number Theory

Factorials

Factorials: Level 1 Challenges

         

6!×7!10!= ? \Large \frac {6! \times 7!}{{10}!} = \ ?

0!+0!+0!+0!0!+0!= ? \Large \frac{0!+0!+0!+0!}{0!+0!}= \ ?

(2015!+2016!2015!×2016!)×2016!= ?\large \left( \frac { 2015!+2016! }{ 2015!\times 2016! } \right) \times 2016! = \ ?

x!=(7!)!7!,       x= ?\Large x! = \frac { (7!)!}{7!}, \ \ \ \ \ \ \ x = \ ?

Evaluate

(10!+9!)(8!+7!)(6!+5!)(4!+3!)(2!+1!)(10!9!)(8!7!)(6!5!)(4!3!)(2!1!).\frac{(10!+9!)(8!+7!)(6!+5!)(4!+3!)(2!+1!)}{(10!-9!)(8!-7!)(6!-5!)(4!-3!)(2!-1!)} .

Hint: You don't need to multiply out all the factorials!

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