Question

Verifica daca 1/21 + 1/22 + ... + 1/30 > 1/3
Prin metoda de majorare

Answer 1

   
Regula:  Dintre 2 fractii cu numaratori egali, este mai mare fractia cu numitorul mai mic.

Rezolvare:
Numarul de termeni este:  30 - 21 + 1 = 9 + 1 = 10 termeni.


[tex]\displaystyle \\ \frac{1}{21} \ \textgreater \ \frac{1}{30}\\\\ \frac{1}{22} \ \textgreater \ \frac{1}{30}\\\\ \frac{1}{23} \ \textgreater \ \frac{1}{30} \\ \\ \cdots \cdots \cdots \cdots \\ \\ \frac{1}{29} \ \textgreater \ \frac{1}{30} \\ \\ \frac{1}{30} = \frac{1}{30} \\ \\ \frac{1}{21} +\frac{1}{22} +\cdots +\frac{1}{30} \ \textgreater \ \frac{1}{21} +\frac{1}{30} +\frac{1}{30} +\cdots +\frac{1}{30} =10\cdot \frac{1}{30}=\frac{10}{30}=\frac{1}{3} \\ \\ \Longrightarrow~~~ \boxed{\frac{1}{21} +\frac{1}{22} +\cdots +\frac{1}{30} \ \textgreater \ \frac{1}{3}}[/tex]