# End of the world

Calculus Level 5

$\large \displaystyle \sum^{\infty}_{a=0} \displaystyle \sum^{\infty}_{b=0} \displaystyle \sum^{\infty}_{c=0}\dfrac{a+b+c+abc} {2^a(2^{a+b}+2^{b+c}+2^{a+c})}$

If the value of above expression is the form of $$\dfrac ab$$, where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

×