Explicație pas cu pas:
[tex]\frac{1}{1\cdot 2} + \frac{1}{2 \cdot 3} + ... + \frac{1}{24 \cdot 25} = \\ [/tex]
[tex]= \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{24} - \frac{1}{25} \\ [/tex]
[tex]= \frac{1}{1} - \frac{1}{25} = \frac{24}{25} \\ [/tex]
[tex]\frac{1}{25\cdot 26} + \frac{1}{26 \cdot 27} + ... + \frac{1}{49 \cdot 50} = \\ [/tex]
[tex]= \frac{1}{25} - \frac{1}{26} + \frac{1}{26} - \frac{1}{27} + ... + \frac{1}{49} - \frac{1}{50} \\ [/tex]
[tex]= \frac{1}{25} - \frac{1}{50} = \frac{1}{50} \\ [/tex]
=>
[tex]x = \sqrt{ \frac{1}{94}\left( \frac{24}{25} - \frac{1}{50} \right)} = \sqrt{ \frac{1}{94} \cdot \frac{48 - 1}{50} } = \\ = \sqrt{ \frac{1}{94} \cdot \frac{47}{50} } = \sqrt{ \frac{1}{100} } = \red{\bf \frac{1}{10}}[/tex]
