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Question
Convert the following products into factorials:
(n + 1) (n + 2) (n + 3) ... (2n)
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Solution
\[\ \left( n + 1 \right)\left( n + 2 \right)\left( n + 3 \right) . . . \left( 2n \right) = \frac{\left( 1 \right)\left( 2 \right)\left( 3 \right) . . . \left( n \right)\left( n + 1 \right)\left( n + 2 \right)\left( n + 3 \right) . . . \left( 2n \right)}{\left( 1 \right)\left( 2 \right)\left( 3 \right) . . . \left( n \right)}\]
\[ = \frac{\left( 2n \right)}{n!}\]
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