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 […]

Recent Comments
 Ron on The art of using the Residue Theorem in evaluating definite integrals
 Konstantinos on The art of using the Residue Theorem in evaluating definite integrals
 Ron on The art of using the Residue Theorem in evaluating definite integrals
 Konstantinos on The art of using the Residue Theorem in evaluating definite integrals
 Ron on Inverse Laplace Transform IV

Meta