100 followers problem

Calculus Level 4

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

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

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