Question

1)Calculati:
a)$\frac{3!+4!+5!}{2!+3!+5!}$
b)$\frac{n!}{(n-3)!}$
c)$\frac{10!-9!}{11!-10!}$
d)$\frac{1}{2!}+ \frac{2}{3!} + \frac{3}{4!}$

Answer 1

a) $\frac{1*2*3+1*2*3*4+1*2*3*4*5}{1*2+1*2*3+1*2*3*4*5} = \frac{6+24+120}{2+6+120} = \frac{150}{128}$
b) - nu stiu
c) $\frac{1*2*3*4*5*6*7*8*9*10 - 1*2*3*4*5*6*7*8*9}{1*2*3*4*5*6*7*8*9*10*11- 1*2*3*4*5*6*7*8*9*10} = \frac{3.628.800-362.880}{39.916.800 - 3.628.800} =$$\frac{3.265.920}{36.288.000}$
d) $\frac{1}{1*2} + \frac{2}{1*2*3} + \frac{3}{1*2*3*4} = \frac{1}{2} + \frac{2}{6} + \frac{3}{24} = \frac{12}{24} + \frac{8}{24} + \frac{3}{24} = \frac{23}{24}$
Exercitiul d l-am amplificat, prima fractie cu 12 iar a doua cu 4 ca sa am factor comun pe 24.