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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