Sylwia83
Rozwiązane

oblicz ile wyrazów ujemnych ma ciag okreslony wzorem
[tex]an = n {2} - 9 {n} + 14[/tex]



Odpowiedź :

[tex]a_{n} = n^{2}-9n+14\\\\n^{2}-9n+14 < 0\\\\\Delta = (-9)^{2}-4\cdot14 = 81 - 56 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5\\\\n \in N+\\\\n_1 = \frac{9-5}{2} =\frac{4}{2}=2, \ \ \ n_2 = \frac{9+5}{2} = \frac{14}{2} = 7\\\\a > 0, \ to \ ramiona \ paraboli \ skierowane \ do \ gory\\\\n \in(2;7)\\\\n \in\{3,4,5,6\}\\\\Wyrazy \ ujemne \ to: \ a_3, a_4, a_5, a_6.[/tex]

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