# Algebra + Calculus = ?

Calculus Level pending

If $T_k= \displaystyle\prod_{r=1}^{j} \tan \left(\dfrac{r\pi}{k}\right) , \ \ \text{where} \ j=\dfrac{k-1}{2};$

Then find the value of $1+\lim_{n \rightarrow \infty}\displaystyle\sum_{m=1}^{n} \dfrac{(-1)^m}{\left(T_{2m+1}\right)^2}$

$$\textbf{Details and Assumptions}$$

$$\bullet \ \ \ \ \displaystyle\prod_{k=1}^{n} a_k=a_1 \cdot a_2 \cdot \ \cdots \ \cdot a_n$$

$$\bullet \ \ \ \ \displaystyle\sum_{k=1}^{n} a_k=a_1+a_2+ \cdots + a_n$$

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