Pergunta

1+(1)/(2)+(1)/(4)+(1)/(8)
Solução

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TatianaMestre · Tutor por 5 anos
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To solve the expression \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}\), we need to add these fractions together.<br /><br />First, let's convert all terms to have a common denominator. The least common denominator for 2, 4, and 8 is 8.<br /><br />1. Convert \(1\) to a fraction with a denominator of 8:<br /> \[<br /> 1 = \frac{8}{8}<br /> \]<br /><br />2. Convert \(\frac{1}{2}\) to a fraction with a denominator of 8:<br /> \[<br /> \frac{1}{2} = \frac{4}{8}<br /> \]<br /><br />3. \(\frac{1}{4}\) already has a denominator of 4, which is a factor of 8:<br /> \[<br /> \frac{1}{4} = \frac{2}{8}<br /> \]<br /><br />4. \(\frac{1}{8}\) already has a denominator of 8:<br /> \[<br /> \frac{1}{8} = \frac{1}{8}<br /> \]<br /><br />Now, add these fractions together:<br />\[<br />\frac{8}{8} + \frac{4}{8} + \frac{2}{8} + \frac{1}{8} = \frac{8 + 4 + 2 + 1}{8} = \frac{15}{8}<br />\]<br /><br />So, the sum of \(1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8}\) is:<br />\[<br />\frac{15}{8}<br />\]<br /><br />In decimal form, this is:<br />\[<br />\frac{15}{8} = 1.875<br />\]<br /><br />Therefore, the correct answer is:<br />\[<br />\boxed{\frac{15}{8}}<br />\]
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