Subjects algebra

Sum 1 To 1000 009F2E

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1. The problem is to find the sum of the series $1 + 2 + 3 + 4 + 5 + \ldots + 1000$. 2. This is an arithmetic series where the first term $a_1 = 1$, the last term $a_n = 1000$, and the number of terms $n = 1000$. 3. The formula for the sum of the first $n$ natural numbers is: $$S_n = \frac{n(n+1)}{2}$$ 4. Applying the formula: $$S_{1000} = \frac{1000(1000+1)}{2}$$ 5. Simplify inside the parentheses: $$S_{1000} = \frac{1000 \times 1001}{2}$$ 6. Now simplify the fraction by canceling common factors: $$S_{1000} = \frac{\cancel{1000} \times 1001}{\cancel{2} \times 1} = 500 \times 1001$$ 7. Multiply to get the final sum: $$S_{1000} = 500 \times 1001 = 500500$$ Therefore, the sum of the numbers from 1 to 1000 is $500500$.