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    "First, let's find the sum of the numbers in Amanda's list. The sum of the first n even numbers is given by the formula n(n+1). In this case, n = 50 (since there are 50 even numbers from 2 to 100). So, the sum of Amanda's list is 50(50+1) = ",
    "Let the roots of the equation be $r, r^2, r^3, r^4, r^5$ in geometric progression. By Vieta's formulas, the sum of the roots is $r + r^2 + r^3 + r^4 + r^5 = 180$. Dividing both sides by $r^5$, we get $1",
    "First, let's find the angle \\( \\angle AOB into three equal parts. The area of each smaller triangle is:\n\\[ \\frac{\\sqrt{3}}{12} \\text{ triangle} = \\frac{\\sqrt{3}/4 \\]\n\nNow, let's find the value of \\( k + m + n \\). We have:\n\\[ k = 1 \\]\n\\["
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