# A problem by Kartik Sharma

Level pending

The sequence $$a_n$$ is defined by $${a}_{1} = 0, |{a}_{2}|=|{a}_{1} + 1|,... |{a}_{n}|= |{a}_{n−1} + 1|$$. If

$\frac{{a}_{1} + {a}_{2} + {a}_{3} + ..... + {a}_{n}}{n} \geq - \frac{a}{b}$

where $$a$$ and $$b$$ are positive coprime integers. Find the value of $$a+b$$.

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