Soal dan Pembahasan Olimpiade Matematika SMA Hasil Kreatifitas Siswa

Pembahasan:
$ \left ( 1-\frac{2}{3} \right )\left ( 1-\frac{2}{5} \right )\left ( 1-\frac{2}{7} \right )\left ( 1-\frac{2}{9} \right ) \cdots \left ( 1-\frac{2}{2013} \right ) $

$ =\left ( \frac{3}{3}-\frac{2}{3} \right )\left ( \frac{5}{5}-\frac{2}{5} \right )\left ( \frac{7}{7}-\frac{2}{7} \right )\left ( \frac{9}{9}-\frac{2}{9} \right ) \cdots \left ( \frac{2013}{2013}-\frac{2}{2013} \right ) $

$ =\left ( \frac{1}{3} \right )\left ( \frac{3}{5} \right )\left ( \frac{5}{7} \right )\left ( \frac{7}{9} \right ) \cdots \left ( \frac{2011}{2013} \right )$
$ =\frac{1}{3} \cdot \frac{3}{5} \cdot \frac{5}{7} \cdot \frac{7}{9} \cdots \frac{2011}{2013}$

$ =\frac{1}{\not{3}} \cdot \frac{\not{3}}{\not{5}} \cdot \frac{\not{5}}{\not{7}} \cdot \frac{\not{7}}{\not{9}} \cdots \frac{\not{2011}}{2013}$

$ =\frac{1}{2013}$

Untuk melihat hasil kreatifitas Simon secara lengkap [Data Disini].


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