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Compute

1 + \frac{3}{6} + \frac{15}{6^2} + \frac{27}{6^3}

 Mar 31, 2024
 #1
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\(1 + \dfrac{3}{6} + \dfrac{15}{6^2} + \dfrac{27}{6^3}\\ =\dfrac{6^3+3\cdot 6^2+15\cdot 6+27}{6^3}\\ =\dfrac{441}{6^3}\\ =\dfrac{3^2\cdot 7^2}{2^3\cdot 3^3}\\ \color{blue}=\dfrac{7^2}{2^3\cdot3}\)

 

laugh !

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 Mar 31, 2024

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