JEE maths#20

Calculus Level 4

f(x)=12+sinx\large f(x) = \frac{1}{ 2+ \lfloor \sin x\rfloor}

If a1 a_1 is the largest value of f(x) f(x) above and an+1=(1)n+2n+1+ana_{n+1} = \dfrac{ (-1)^{n+2} }{n+1} + a_{n} , for n1n \ge 1, find the value of limnan\displaystyle \lim_{n \to \infty} a_{n}.

Notation: \lfloor \cdot \rfloor denotes the floor function.

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