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Call a positive integer \(N\) a \(q\)-sum if it can be written as the sum of \(q\) consecutive positive integers. For example, \(15\) is a \(2\)-sum because ...

The length \((L)\) and width \((W)\) of a rectangle are random variables, independently and uniformly distributed on the interval \([9,11],\) and the area \((A)\) of the rectangle is also ...

Let \(s(n)\) be the sum of the digits of \(n\)'s base-\(2017\) representation. Compute the sum \[ \sum_{n = 1}^{\infty} \frac{s(n)}{n(n+1)}.\]

Round your ...

\[ \displaystyle \sum_{k=1}^{n} x_k^J \le \sum_{k=1}^n \dfrac{1}{x_k^J}\]

Given that \(J=\frac{3}{2}\) and that \(x_1,x_2, \ldots,x_n\) are positive ...

\[\sum_{k=1}^{n} x_k^2 \le \sum_{k=1}^n \dfrac{1}{x_k^2}\]

Given that \(x_1,x_2, \ldots,x_n\) are positive reals whose sum is \(n\), find the ...

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