Question

решите:

1) n!/(n-1)!

2) (2л+1)!.(2л-1)!

3) n!=7(n-1)!

4) (m+17)!=420(m+15)!

Answer 1

 

$1) frac{n!}{(n-1)!} = frac{1*2*...*(n-1)*n}{1*2*...*(n-1)} = n\\ 2) frac{(2n+1)!}{(2n-1)!} = frac{1*2*...*(2n-1)*2n*(2n+1)}{1*2*...*(2n-1)} = 2n(2n+1) = 4n^2+2n\\ 3) n!=7(n-1)!\ frac{n!}{(n-1)!} = 7\ frac{1*2*...*(n-1)*n}{1*2*...*(n-1)} = 7\ n = 7$

 

 

 

$4) (m+17)!=420(m+15)!\ frac{(m+17)!}{(m+15)!} = 420\ frac{1*2*...*(m+15)*(m+16)*(m+17)}{1*2*...*(m+15)} = 420\ (m+16)*(m+17) = 420\ m^2+16m+17m+16*17 = 420\ m^2+33m + 272 - 420 = 0\ m^2+33m-148 = 0\ m_1*m_2 = -148\ m_1+m_2 = -33\ m_1 = -37, m_2 = 4\ m = 4$