# Can you generalize this?

Algebra Level 5

$\dfrac1{1\cdot3} + \dfrac2{1\cdot3\cdot5} + \dfrac3{1\cdot3\cdot5\cdot7} + \cdots$

If the sum above can be expressed as $\dfrac AB$, where $B$ is a prime and $A$ is a positive integer, find $(A+B)!$.

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