Question

A expressão:

(K+2)!-k!/(k+1)!-k


para K € N*, equivale a:

a)(K+2)!/(K+1)!

b) K^2+3k+1/k

c) k+2/k+1

d) 2
e) k^2+2k/k-1


Preciso da resolução!!

Answer 1

• $n!=n.(n-1)(n-2)...(n-k)...1$

• $a.b+ac=a(b+c)$

$\frac{(k+2)!-k!}{(k+1)!-k!}\\\\\frac{(k+2)(k+1)k!-k!}{(k+1)k!-k!}\\\\\frac{k![(k+2)(k+1)-1]}{k![(k+1)-1]}\\\\\frac{(k+2)(k+1)-1}{(k+1)-1}\\\\\frac{k^2+k+2k+2-1}{k}\\\\\frac{k^2+3x+1}{k}$