Problem: evaluate the following sum… $$\sum_{k=0}^{\infty}\dfrac{(1)^{\frac{k(k+1)}{2}}}{(2k+1)^2}$$ This is unusual because the $1$ is raised to the $k (k+1)/2$ power, rather than the usual $k$th power. On the surface, this problem may look hopeless, but really, it is all about determining the pattern of odd and even numbers from the sequence $k (k+1)/2$, which turns out […]

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