1. **State the problem:** We are given the function $$f(x) = \frac{x(x+1)(2x+1)}{6}$$ and asked to evaluate it at $$x=100$$. 2. **Formula and explanation:** This function is a known formula for the sum of the squares of the first $$x$$ natural numbers: $$1^2 + 2^2 + \cdots + x^2 = \frac{x(x+1)(2x+1)}{6}$$. 3. **Substitute $$x=100$$ into the formula:** $$f(100) = \frac{100 \times 101 \times 201}{6}$$ 4. **Calculate step-by-step:** - Multiply numerator terms: $$100 \times 101 = 10100$$ - Then $$10100 \times 201 = 2,030,100$$ - Divide by 6: $$\frac{2,030,100}{6} = 338,350$$ 5. **Final answer:** $$f(100) = 338,350$$ This means the sum of squares from 1 to 100 is 338,350.