Question

Ciagi.Rozwiaz

1) lim [tex]\frac{2^{1/n} -1}{4^{1/n} -1}[/tex]

2) lim [tex]\frac{n!(n^{2}+1) }{(n+2)!}[/tex]

Answer 1

Odpowiedź:

1 )        = [tex]\lim_{n \to \infty} \frac{1}{2^{1/n} + 1} = \frac{1}{2}[/tex]

2 )   = [tex]\lim_{n \to \infty} \frac{n^2 + 1}{( n +1)*(n + 2)} = lim \frac{1 + \frac{1}{n^2} }{(1 + \frac{1}{n})*(1 + \frac{2}{n} )} =[/tex] [tex]\frac{1}{1*1} = 1[/tex]

Szczegółowe wyjaśnienie:

[tex]4^{1/n} - 1 = ( 2^{1/n} - 1)*( 2^{1/n} + 1)[/tex]