# There's something hidden in it

Calculus Level 4

${a}_{n+1} +1 = (n+1){a}_{n}$

Define an sequence $$\lbrace a_{n} \rbrace_{n=0}$$ by the iteration above. For what value of $${a}_{0}$$ will the iteration converge to some finite value?

Report your answer as first four digits of $${a}_{0}$$ (without rounding off). For example, if your answer is $$3.141592653789 \ldots$$ then enter 3.141.

Interestingly in the complete number line there exists only one possible value of $${a}_{0}$$, for which this iteration doesn't diverge (that's the interesting aspect of it)

The sequence diverge to positive infinity for any starting value larger than $$a_0$$, and the sequence diverge to negative for any starting value smaller than $$a_0$$.

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