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f(x)=12+⌊sinx⌋\large f(x) = \frac{1}{ 2+ \lfloor \sin x\rfloor}f(x)=2+⌊sinx⌋1
If a1 a_1 a1 is the largest value of f(x) f(x) f(x) above and an+1=(−1)n+2n+1+ana_{n+1} = \dfrac{ (-1)^{n+2} }{n+1} + a_{n} an+1=n+1(−1)n+2+an, for n≥1n \ge 1n≥1, find the value of limn→∞an\displaystyle \lim_{n \to \infty} a_{n}n→∞liman.
Notation: ⌊⋅⌋ \lfloor \cdot \rfloor ⌊⋅⌋ denotes the floor function.
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