# Is it complicated or complex?

Calculus Level 4

$\mathscr{E} = \displaystyle \sum_{n=0}^{\infty} \dfrac{\sin \left( \dfrac{\pi n}{2} + \dfrac{\pi}{4}\right) }{2^n}$

If $$\mathscr{E}$$ can be represented in the form $$\dfrac{a \sqrt{b}}{c}$$, with $$a, c$$ coprime positive integers and $$b$$ square free, find $$a + b + c$$.

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