Question

Va rog sa ma ajutati cu astea:
a) (n+1)! supra n!
b) (n+3)! supra n!(n+3)
c) (n+1)!n! supra (n-1)!(n+2)!

Answer 1

a) $\frac{(n+1)!}{n!} = \frac{n!(n+1)}{n!} = n+1$
b) $\frac{(n+3)!}{n!(n+3)} = \frac{n!(n+1)(n+2)(n+3)}{n!(n+3)} = (n+2)(n+3) = n^{2}+5n+6$
c) $\frac{(n+1)!n!}{(n-1)!(n+2)!} = \frac{(n-1)!n(n+1)n!}{(n-1)!n!(n+1)(n+2)}= \frac{n}{n+2}$