CEMC Fryer, 2005

Algebra Difficulty 1.0 Junior Prove it Canada

When the super-sum of a new line segment $AJ$ with 9 basic sub-segments of lengths from left to right of $1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}, \frac{1}{9}$ is calculated, the answer is $45$ . Determine the super-sum of a line segment $AP$ with 15 basic sub-segments of lengths from left to right of $1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{15}$ .

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