Question

x*2(1/1*2+1/2*3+1/3*2+...+1/99*100)=99 aflati x

Answer 1

Explicație pas cu pas:

$x \times 2\left( \frac{1}{1\cdot 2} + \frac{1}{2 \cdot 3} + ... + \frac{1}{98 \cdot 99} + \frac{1}{99 \cdot 100}\right) = 99$

$x \times 2 \left( \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{98} - \frac{1}{99} + \frac{1}{99} - \frac{1}{100} \right) = 99$

$x \times 2\left( \frac{1}{1} - \frac{1}{100} \right) = 99$

$x \times \frac{2 \times 99}{100} = 99 \implies x = 50$