Question

calcule a soma dos 10 primeiros termos da pg (1, ½ , ¼ , ⅛...)

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Answer 1

$> resolucao \\ \\ \geqslant progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} \\ q = \frac{ \frac{1}{2} }{1} \\ q = \frac{1}{2} \times 1 \\ q = \frac{1}{2} \\ \\ \\ \\ sn = \frac{a1(1 - q {}^{n} )}{1 - q} \\ \\ sn = \frac{1(1 - ( \frac{1}{2}) {}^{10}) }{1 - \frac{1}{2} } \\ \\ sn = \frac{1(1 - \frac{1}{1024} )}{ \frac{1}{2} } \\ \\ sn = \frac{1 \times \frac{1023}{1024} }{ \frac{1}{2} } \\ \\ sn = \frac{ \frac{1023}{1024} }{ \frac{1}{2} } \\ \\ sn = \frac{1023}{1024} \times \frac{2}{1} \\ \\ sn = \frac{2046 \div 2}{1024 \div 2} \\ \\ sn = \frac{1023}{512} \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$