# 400 Followers Problem - Reciprocal Summations 2

Calculus Level 5

$\large{S = \left( 1 + \dfrac{1}{2} + \dfrac{1}{3} \right) - \left( \dfrac{1}{4} + \dfrac{1}{5} + \dfrac{1}{6} \right) + \left( \dfrac{1}{7} + \dfrac{1}{8} + \dfrac{1}{9} \right) - \left( \dfrac{1}{10} + \dfrac{1}{11} + \dfrac{1}{12} \right) + \ldots }$

If $$S$$ can be expressed as:

$\large{\dfrac{A\sqrt{B}}{C}\pi^D + \dfrac{\ln(E)}{F} }$

for positive integers $$A,B,C,D,E,F$$ where $$\gcd(A,C)=1$$ and $$B,E$$ aren't any $$m^{th}$$ power of a positive integer with $$m \in \mathbb Z, \ m \geq 2$$.

Submit the value of $$A+B+C+D+E+F$$ as your answer.

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