Question

Aratati ca x este numar rational.​

Answer 1

Răspuns:

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Answer 2

Explicație pas cu pas:

$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + ... + \frac{1}{24 \times 25} = \\ = \left(\frac{1}{1} - \frac{1}{2} \right) + \left(\frac{1}{2} - \frac{1}{3} \right) + ... + \left(\frac{1}{24} - \frac{1}{25} \right) \\ = \frac{1}{1} - \frac{1}{25} = \frac{25 - 1}{25} = \frac{24}{25}$

$\frac{1}{25 \times 26} + \frac{1}{26 \times 27} + ... + \frac{1}{49 \times 50} = \\ = \left(\frac{1}{25} - \frac{1}{26} \right) + \left(\frac{1}{26} - \frac{1}{27} \right) + ... + \left(\frac{1}{49} - \frac{1}{50} \right) \\ = \frac{1}{25} - \frac{1}{50} = \frac{2 - 1}{50} = \frac{1}{50}$

$x = \sqrt{ \frac{1}{94}\left( \frac{24}{25} - \frac{1}{50} \right) } = \sqrt{ \frac{1}{94} \times \frac{48 - 1}{50} } \\ = \sqrt{ \frac{47}{94 \times 50} } = \sqrt{ \frac{1}{100} } = \frac{1}{10}$