Răspuns:
c) [tex]\frac{17^{n+2}-5*17^{n+1}+17^{n}}{3*19^{n+1}-90*19^{n}+19^{n+2} } =\frac{17^{n}(17^{2} -5*17+17)}{19^{n}(3*19-90+19^{2}) } =\frac{17^{n}(289-85+17)}{19^{n}(57-90+361) } =\frac{17^{n}*205(41}{19^{n}*328} =\frac{17^{n}*5}{19^{n}*8}[/tex]
d) [tex]\frac{5*4^{n}*3^{n+1}+4^{n+1}*3^{n+2}}{12^{n+1}+5*12x^{n} }= \frac{4^{n}*3^{n+1}(5*+4*3)}{12^{n}(12+5)}=\frac{4^{n}*3^{n}*3*17(4^{n}*3^{n}*17}{4^{n}*3^{n}*17}=3[/tex]∈ N
e) [tex]\frac{2^{n}*3^{n+1}+2^{n+2}*3^{n}}{3^{n}*5^{n+1}+3^{n+2}*5^{n}} =\frac{2^{n}*3^{n}(3+2^{2})(3^{n} }{3^{n}*5^{n}(5+3^{2})}} =\frac{2^{n}*7(14}{5^{n}*14}} =\frac{2^{n-1}}{5^{n}}}[/tex] ireductibila
Explicație pas cu pas:
