Synthetic infinite product

Algebra Level 5

$\large \left \lfloor 100 \prod_{i=1}^\infty \left(1 + \frac1{a_i} \right) \right \rfloor$

Consider the recurrence relation $$a_{i+1} = i (1+a_i)$$ with initial term $$a_1 = 1$$, what is the value of the expression above?

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