Faulty Factorials

Number Theory Level 2

\[ \begin{array} { l l r } 1! \times 3! & = (1+2)! & \{1\} \\ 1! \times 3! \times 5! & = (1+2+3)! & \{2\} \\ 1! \times 3! \times 5! \times 7! & = (1+2+3 + 4)! & \{3\} \\ 1! \times 3! \times 5! \times 7! \times 9! & = (1+2+3 + 4 + 5)! \quad\quad & \{4\} \\ \end{array} \]

Which of the above equations is false?

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