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Question
Prove that
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Solution
\[LHS = \frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!}\]
\[ = \frac{1}{9!} + \frac{1}{10 \times 9!} + \frac{1}{11 \times 10 \times 9!}\]
\[ = \frac{110 + 11 + 1}{11 \times 10 \times 9!}\]
\[ = \frac{122}{11!} = RHS \hspace{0.167em} \]
\[\text{Hence, proved} .\]
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