Question

sa se aduca la o forma cat mai simpla:
123!/121!
(n+1)!/n!
(n+3)!/n!(n+3)
(n+1)!n!/(n-1)!(n+2)!

Answer 1

   
[tex]\displaystyle\\ \frac{123!}{121!}=\frac{121! \times 122 \times 123}{121!}= 122 \times 123 = \boxed{\bf 15006}\\\\\\ \frac{(n+1)!}{n!} = \frac{n!\times(n+1)}{n!} =\boxed{\bf n+1}\\\\\\ \frac{(n+3)!}{n! \times (n+3)}=\frac{n! \times(n+1)(n+2)(n+3)}{n! \times (n+3)}=\boxed{\bf (n+1)(n+2)}\\\\\\ \frac{(n+1)! \times n!}{(n-1)!\times(n+2)!}= \frac{n!}{(n-1)!}\times \frac{(n+1)!}{(n+2)!}=\\\\ = \frac{(n-1)!\times n}{(n-1)!}\times \frac{(n+1)!}{(n+1)! \times (n+2)}= \boxed{\bf \frac{n}{n+2}} [/tex]