1. The problem asks to find the sum of the sequence $1 + 2 + 3 + \dots + 1001$ and determine which of the given numbers it is divisible by. 2. The sum of the first $n$ natural numbers is given by the formula: $$ S = \frac{n(n+1)}{2} $$ 3. Here, $n = 1001$, so substitute this into the formula: $$ S = \frac{1001 \times 1002}{2} $$ 4. Calculate the numerator: $$ 1001 \times 1002 = 1003002 $$ 5. Divide by 2: $$ S = \frac{1003002}{2} = 501501 $$ 6. Now, check divisibility by each given number: - Divisible by 1005? $$ \frac{501501}{1005} = 499.5 \quad \text{(not an integer)} $$ - Divisible by 1003? $$ \frac{501501}{1003} = 500 \quad \text{(an integer)} $$ - Divisible by 1001? $$ \frac{501501}{1001} = 501 \quad \text{(an integer)} $$ 7. Since $501501$ is divisible by both $1003$ and $1001$, but not by $1005$, the correct answers are divisibility by $1003$ and $1001$. Final answer: The sum is divisible by 1003 and 1001.