# Inspired By Shubhendra Singh

$\large \dfrac{1}{2^3 \times3!}-\dfrac{1\times 3}{2^4\times 4!}+\dfrac{1\times3\times5}{2^5\times5!} - \ldots$

If the alternating series above equals to $$\dfrac A{24} - \dfrac B{B+1} \sqrt2$$ for positive integers $$A$$ and $$B$$, find the value of $$A+B$$.

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