1. The problem asks us to evaluate the sum $$\sum_{k=1}^{15} \frac{1}{k}$$ which means adding the reciprocals of all integers from 1 to 15. 2. The formula for this sum is the partial sum of the harmonic series: $$H_n = \sum_{k=1}^n \frac{1}{k}$$ where $n=15$. 3. We calculate each term and add: $$1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11} + \frac{1}{12} + \frac{1}{13} + \frac{1}{14} + \frac{1}{15}$$ 4. Adding these fractions (using decimal approximations): $$1 + 0.5 + 0.3333 + 0.25 + 0.2 + 0.1667 + 0.1429 + 0.125 + 0.1111 + 0.1 + 0.0909 + 0.0833 + 0.0769 + 0.0714 + 0.0667 \approx 3.3182$$ 5. Therefore, the value of the sum is approximately $$3.3182$$. This sum is known as the 15th harmonic number $H_{15}$.