Queen of the limit

Algebra Level 4

12+12+1100+12+2100+12+3100+...+12+299100= ?\large{ \left\lceil \frac{1}{2} \right\rceil + \left\lceil \frac{1}{2} +\frac{1}{100}\right\rceil +\left\lceil \frac{1}{2} + \frac{2}{100}\right\rceil +\left\lceil \frac{1}{2} + \frac{3}{100} \right\rceil +...+\left\lceil \frac{1}{2} + \frac{299}{100} \right\rceil = \ ?}

Note: x \left\lceil x \right\rceil denotes the ceiling function, which is defined as the smallest integer that not less than xx.

Bonus: How did I name the problem?

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