Question

18 puncte .... Sa se calculeze suma
$1 + \frac{1}{2} + \frac{1}{ {2}^{2} } + ... + \frac{1}{ {2}^{7} }$

Answer 1

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Answer 2

[tex]\text{Suma este o progresie geometrica de ratie 1/2.}\\ S=1+\dfrac{1}{2}+\dfrac{1}{2^2}+_{\dots}+\dfrac{1}{2^7}\\ S=\dfrac{\left(\dfrac{1}{2}\right)^8-1}{\dfrac{1}{2}-1}=2\left(1-\left(\dfrac{1}{2}\right)^8\right)[/tex]