Subjects algebra

Sum 194 440E81

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1. The problem is to find the sum of the first 194 natural numbers. 2. The formula for the sum of the first $n$ natural numbers is: $$S = \frac{n(n+1)}{2}$$ where $S$ is the sum and $n$ is the number of terms. 3. Substitute $n = 194$ into the formula: $$S = \frac{194(194+1)}{2}$$ 4. Simplify inside the parentheses: $$S = \frac{194 \times 195}{2}$$ 5. Multiply the numerator: $$194 \times 195 = 37830$$ 6. Now divide by 2: $$S = \frac{37830}{2}$$ 7. Use the cancellation notation: $$S = \frac{\cancel{37830}}{\cancel{2}} = 18915$$ 8. Therefore, the sum of the first 194 natural numbers is $18915$.