There's something hidden in it

Calculus Level 5

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

Define an sequence {an}n=0\lbrace a_{n} \rbrace_{n=0} by the iteration above. For what value of a0{a}_{0} will the iteration converge to some finite value?

Report your answer as first four digits of a0{a}_{0} (without rounding off). For example, if your answer is 3.1415926537893.141592653789 \ldots then enter 3.141.

Interestingly in the complete number line there exists only one possible value of a0{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 a0a_0, and the sequence diverge to negative for any starting value smaller than a0a_0 .


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