# Not an usual Trigonometric Summation!

Calculus Level 5

$\large{L = \lim_{n \to \infty} \sum_{k=1}^n \dfrac{1}{2^k} \tan\left(\dfrac{\pi}{3\cdot2^{k+1}}\right)}$

If $$L$$ can be represented as:

$\large{\dfrac{A}{\pi^B} - \sqrt{C}}$

where $$A,B,C$$ are positive integers, find the value of $$A+B+C$$?

###### Here is a similar problem : Limited Trigonometry.
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