# I haven't seen it before 2

Calculus Level 5

Let $$\mathfrak P_n=\dfrac 1n+\dfrac{1}{3n^3}+\dfrac{1}{5n^5}+\dfrac{1}{7n^7} + \cdots$$.

If the value of $$\displaystyle\sum_{n=2}^{99}\ 2\mathfrak{P}_n$$ is equal to $$\ln\alpha$$, find $$\alpha$$.

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