Question

Ex 26 , Sa se calculeze suma prin progresie

Answer 1

este o suma de 8 termeni in progresie geometrica, cu primul termen =1, si ratia
$\frac{1}{2}$
$1 + \frac{1}{2} + ... + \frac{1}{ {2}^{7} } = \\ 1 \times \frac{? \1 - { \frac{1}{2} }^{8} }{1 - \frac{1}{2} }$
$1\times \frac{ 1 - ({ \frac{1}{2})}^{8} }{1 - \frac{1}{2} } =$
$\frac{1 - \frac{1}{ {2}^{8} } }{1 - \frac{1}{2} } = \frac{ {2}^{8} - 1}{ {2}^{8} \times \frac{1}{2} } = \frac{ {2}^{8} - 1 }{ {2}^{7} } = \frac{256 - 1}{128 } = \frac{255}{128}$