1. The problem involves sequences or sets of fractions: (i) $\frac{2}{5}, \frac{2}{5}, \frac{1}{5}$; (ii) $\frac{1}{5}, \frac{1}{2}, \frac{3}{5}$. We analyze each part separately. 2. (i) The fractions $\frac{2}{5}, \frac{2}{5}, \frac{1}{5}$ can be considered values in a sequence or probabilities. We note that $\frac{2}{5} + \frac{2}{5} + \frac{1}{5} = \frac{5}{5} = 1$, confirming they form a partition of 1. 3. (ii) The fractions $\frac{1}{5}, \frac{1}{2}, \frac{3}{5}$ sum to $\frac{1}{5} + \frac{1}{2} + \frac{3}{5} = \frac{2}{10} + \frac{5}{10} + \frac{6}{10} = \frac{13}{10} = 1.3$, which is greater than 1. 4. (iii) If these fractions represent probabilities or weights, (i) could represent a proper distribution while (ii) would not since the sum exceeds 1. Final answer: (i) The sum is 1, a valid partition. (ii) The sum is 1.3, not a valid partition. (iii) Only (i) forms a proper partition of 1.