Question

Determinati numarul a= radical 1/2ori [1/1ori 2+1/ 2ori 3+1/3ori 4+. +1/48ori49+1/49ori 50].

Answer 1

Explicație pas cu pas:

$a = \sqrt{ \dfrac{1}{2} \cdot \Big( \dfrac{1}{1 \cdot 2} + \dfrac{1}{2 \cdot 3} + \dfrac{1}{3 \cdot 4} + ... + \dfrac{1}{48 \cdot 49} + \dfrac{1}{49 \cdot 50}\Big)} = \\ = \sqrt{ \dfrac{1}{2} \cdot \Big( \dfrac{2 - 1}{1 \cdot 2} + \dfrac{3 - 2}{2 \cdot 3} + \dfrac{4 - 3}{3 \cdot 4} + ... + \dfrac{49 - 48}{48 \cdot 49} + \dfrac{50 - 49}{49 \cdot 50}\Big)} \\ = \sqrt{ \dfrac{1}{2} \cdot \Big( \dfrac{1}{1} - \dfrac{1}{2} + \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{4} + ... + \dfrac{1}{48} - \dfrac{1}{49} + \dfrac{1}{49} - \dfrac{1}{50}\Big)}$

$= \sqrt{ \dfrac{1}{2} \cdot \Big( \dfrac{1}{1} - \dfrac{1}{50}\Big)} = \sqrt{ \dfrac{1}{2} \cdot \dfrac{50 - 1}{50}}$

$= \sqrt{ \dfrac{1}{2} \cdot \dfrac{49}{50}} = \sqrt{\dfrac{ {7}^{2} }{ {10}^{2} }} = \bf \dfrac{7}{10}$

Answer 2

Bună, sper ca te am ajutat!!