Question

se considera a=2/1x3 + 2/3x5 ....+2/49x51 stabiliti daca a € 1/2,1
dau coroana daca se poa si oleak explicat

Answer 1

Explicație pas cu pas:

$a = \dfrac{2}{1 \cdot 3} + \dfrac{2}{3 \cdot 5} + ... + \dfrac{2}{49 \cdot 51} = \dfrac{3 - 1}{1 \cdot 3} + \dfrac{5 - 3}{3 \cdot 5} + ... + \dfrac{51 - 49}{49 \cdot 51} = \dfrac{1}{1} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + ... + \dfrac{1}{49} - \dfrac{1}{51} = \dfrac{1}{1} - \dfrac{1}{51} = \dfrac{51 - 1}{51} = \bf \dfrac{50}{51}$

$\dfrac{1}{2} = \dfrac{50}{100} \implies \dfrac{1}{2} < \dfrac{50}{51} < 1 \\ \implies \dfrac{1}{2} < a < 1$

$\implies a \in \Big(\dfrac{1}{2} ; 1\Big)$