# Limit of an infinite Summation!

Calculus Level 4

$\Large{ L = \lim_{a \to 0^+} \left[ \sum_{n=0}^\infty \dfrac{(2n+1)a^2 + (-1)^n}{(2n+1)e^{(2n+1)a}} \right]}$

If $$L$$ can be expressed as $$\dfrac{A}{B} \pi^C$$ for positive integers $$A,B,C$$ such that $$\gcd(A,B) = 1$$, then find the value of $$A+B+C$$.

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