Question

determine o valor de m, sabendo que
$2 + \frac{4}{m} + \frac{8}{m {}^{2} } + ... = \frac{14}{5}$
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Answer 1

$2 + \frac{4}{m}+\frac{8}{m^2}+...=\frac{14}{5}\\\\P.G(2, \frac{4}{m}, \frac{8}{m^2},...)\\\\q=\frac{4}{m}\div2=\frac{4}{2m}=\frac{2}{m}\\\\Soma \ dos \ termos \ infinitos: S= \frac{a_1}{1-q}\\\\ \frac{2}{1-\frac{2}{m}}=\frac{14}{5}\\\\14(1-\frac{2}{m})=5\cdot2\\\\14-\frac{28}{m}=10\\\\14m-28=10m\\\\14m-10m=28\\\\4m=28\\\\m=\frac{28}{4}\\\\ \boxed{m=7}$