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Let \(S\) be the set of pairs of real numbers \((x,y)\) such that for at least one pair of positive integers \(m,n\),

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\[ \large \prod _{ n=1 }^{ \infty }{ \left( 1+\frac { 1 }{ \left\lfloor \sqrt [ 100 ]{ n } \right\rfloor } \right) }^{(-1)^{n-1}} =\frac { \pi }{ a } \]

Find the value of \(a\) that satisfies ...

Let \( f(x) = (x+1)(x+2)(x+3)(x+4) + 5 \), where \( x \in [-6, 6 ] \).

If the range of the function is \( [ a, b ] \), what is the value ...

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