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 \(\alpha\).


Try the Part-1 here.
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