Question

12 b repede daca se poate
mutumesc

Answer 1

Răspuns:

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Explicație pas cu pas:

$\dfrac{1}{4*5}+\dfrac{1}{5*6}+\dfrac{1}{6*7}+...+\dfrac{1}{23*24}=\\=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{23}-\dfrac{1}{24}=\dfrac{1}{4}-\dfrac{1}{24}=\dfrac{6}{24}-\dfrac{1}{24}=\dfrac{5}{24}\\\dfrac{1}{8}=\dfrac{3}{24},~~~\dfrac{1}{4}=\dfrac{6}{24}$

Intervalul (1/8; 1/4)=(3/24; 6/24).  Deoarece 3/24<5/24<6/24, ⇒

5/24 ∈ (3/24; 6/24), deci  5/24 ∈  (1/8; 1/4).