Subjects algebra

Sum First 100 1E2538

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1. **State the problem:** We need to find the sum of the first 100 whole numbers. 2. **Identify the formula:** From the pattern, the sum of the first $n$ whole numbers is given by the formula: $$\text{Sum} = \frac{n \times (n + 1)}{2}$$ This formula comes from the observation that the sum of numbers from 1 to $n$ can be paired to form $n$ pairs each summing to $n+1$, then divided by 2 to avoid double counting. 3. **Apply the formula for $n=100$:** $$\text{Sum} = \frac{100 \times (100 + 1)}{2}$$ 4. **Simplify inside the parentheses:** $$\text{Sum} = \frac{100 \times 101}{2}$$ 5. **Calculate the numerator:** $$\text{Sum} = \frac{10100}{2}$$ 6. **Divide numerator and denominator by 2:** $$\text{Sum} = \frac{\cancel{10100}^{5050}}{\cancel{2}^1} = 5050$$ 7. **Final answer:** The sum of the first 100 whole numbers is **5050**.