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I(r,n)=∫−∞0xrenx dx\displaystyle I(r,n)=\int _{ -\infty }^{ 0 }{ { x }^{ r }{ e }^{ nx } \text{ d}x } I(r,n)=∫−∞0xrenx dx where r,n∈Zr,n \in \mathbb{Z} r,n∈Z.
X=∑n=1∞∑r=0∞1I(r,n)\displaystyle X= \sum_{n=1}^{\infty } \sum_{r=0}^{\infty } \frac{1}{I(r,n)}X=n=1∑∞r=0∑∞I(r,n)1
Find ⌊104X⌋\left\lfloor { 10 }^{ 4 }X \right\rfloor⌊104X⌋
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