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\(Compute \frac{3}{4}\cdot \frac{8}{9}\cdot \frac{15}{16}\cdot \frac{24}{25}\cdot \frac{35}{36}\cdot \frac{48}{49}\cdot \frac{63}{64}\cdot \frac{80}{81}\cdot \frac{99}{100}.\)

Express your answer in the simplest way possible

 Oct 19, 2019
 #1
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3/4×8/9×15/16×24/25×35/36×48/49×63/64×80/81×99/100

 

= 11 / 20

 Oct 19, 2019
 #2
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Compute

\(\dfrac{3}{4}\cdot \dfrac{8}{9}\cdot \dfrac{15}{16}\cdot \dfrac{24}{25}\cdot \dfrac{35}{36}\cdot \dfrac{48}{49}\cdot \dfrac{63}{64}\cdot \dfrac{80}{81}\cdot \dfrac{99}{100}\).

 

\(\begin{array}{|rcll|} \hline && \mathbf{\dfrac{3}{4}\cdot \dfrac{8}{9}\cdot \dfrac{15}{16}\cdot \dfrac{24}{25}\cdot \dfrac{35}{36}\cdot \dfrac{48}{49}\cdot \dfrac{63}{64}\cdot \dfrac{80}{81}\cdot \dfrac{99}{100} } \\\\ &=& \dfrac{1\cdot3}{2\cdot2}\cdot \dfrac{2\cdot4}{3\cdot3}\cdot \dfrac{3\cdot5}{4\cdot4}\cdot \dfrac{4\cdot6}{5\cdot5}\cdot \dfrac{5\cdot7}{6\cdot6}\cdot \dfrac{6\cdot8}{7\cdot7}\cdot \dfrac{7\cdot9}{8\cdot8}\cdot \dfrac{8\cdot10}{9\cdot9}\cdot \dfrac{9\cdot11}{10\cdot10} \\\\ &=& \dfrac{1}{2}\cdot \dfrac{2}{2}\cdot \dfrac{3}{3}\cdot \dfrac{3}{3}\cdot \dfrac{4}{4}\cdot \dfrac{4}{4}\cdot \dfrac{5}{5}\cdot \dfrac{5}{5}\cdot \dfrac{6}{6}\cdot \dfrac{6}{6}\cdot \dfrac{7}{7}\cdot \dfrac{7}{7}\cdot \dfrac{8}{8}\cdot \dfrac{8}{8}\cdot \dfrac{9}{9}\cdot \dfrac{10}{10}\cdot \dfrac{11}{10} \\\\ &=& \dfrac{1}{2}\cdot \dfrac{11}{10} \\\\ &=& \mathbf{ \dfrac{11}{20} } \\ \hline \end{array} \)

 

laugh

 Oct 20, 2019

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