Question

cine ma ajuta cu ex 3​

Answer 1

Explicație pas cu pas:

$S = \dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4} + ... + \dfrac{50}{51}$

$\dfrac{1}{2} \leqslant \dfrac{1}{2} < 1$

$\dfrac{1}{2} < \dfrac{2}{3} < 1$

$\dfrac{1}{2} < \dfrac{3}{4} < 1$

...

$\dfrac{1}{2} < \dfrac{50}{51} < 1$

adunăm:

$\underbrace{\dfrac{1}{2} + \dfrac{1}{2} + ... + \dfrac{1}{2}}_{50 \ \ termeni} < \underbrace{\dfrac{1}{2} + \dfrac{2}{3} + \dfrac{3}{4} + ... + \dfrac{50}{51}}_{50 \ \ termeni} < \underbrace{1 + 1 + 1 + ... + 1}_{50 \ \ termeni}$

$\implies \dfrac{50}{2} < S < 50 \cdot 1 \iff 25 < S < 50$

$\implies \bf S \in \Big(25; 50\Big)$

q.e.d.