Question

Sa se calculeze:
a)15!/21!
b)(n+2)!/n!
c)n/n!+(n^2+n)/(n+1)!-2/(n-1)!

Answer 1

a)$\frac{15!}{21!} = \frac {15!}{15!*16*17*...*21} = \frac{1}{16*17*...*21}$


b)$\frac{(n+2)!}{n!} = \frac{n!*(n+1)*(n+2)}{n!} = (n+1)(n+2)$


c)
[tex]\frac{n}{n!} + \frac{n^{2}+n}{(n+1)!} -2\frac{1}{(n-1)!} = \frac{n}{n*(n-1)!} + \frac{n(n+1)}{n!*(n+1)} - 2\frac{1}{(n-1)!} = \\\\ = 2\frac{n}{n*(n-1)!} - 2\frac{1}{(n-1)!} = 0 [/tex]

La ultimul punct am mai sarit din etape ca era prea mult de editat daca nu ai inteles concrect intreaba.