Question

cine mă poate ajuta repede desi coroana​

Answer 1

Explicație pas cu pas:

a)

$x = \sqrt{ \dfrac{74}{71} \cdot \bigg[\bigg(\dfrac{1}{1 \cdot 2} + \dfrac{1}{2 \cdot 3} + ... + \dfrac{1}{36 \cdot 37}\bigg) - \bigg(\dfrac{1}{37 \cdot 38} + \dfrac{1}{38 \cdot 39} + ... + \dfrac{1}{73 \cdot 74}\bigg)\bigg]} =$

$= \sqrt{ \dfrac{74}{71} \cdot \bigg[\bigg(\dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{4} + ... + \dfrac{1}{35} - \dfrac{1}{36} + \dfrac{1}{36} - \dfrac{1}{37}\bigg) - \bigg(\dfrac{1}{37} - \dfrac{1}{38} + \dfrac{1}{38} - \dfrac{1}{39} + ... + \dfrac{1}{73} - \dfrac{1}{74}\bigg)\bigg]} =$

$= \sqrt{ \dfrac{74}{71} \cdot \bigg(\dfrac{37 - 1}{37} - \dfrac{2 - 1}{74}\bigg)} = \sqrt{ \dfrac{74}{71} \cdot \bigg(\dfrac{36}{37} - \dfrac{1}{74}\bigg)}$

$= \sqrt{ \dfrac{74}{71} \cdot \dfrac{72 - 1}{74}} = \sqrt{ \dfrac{74}{71} \cdot \dfrac{71}{74}} = \sqrt{1} = \bf 1$