Finite sums
Posted: Mon Nov 09, 2015 5:04 pm
These are two well known sums, but let them exist here as well.
a) $\displaystyle \sum_{k=1}^{m} \tan^2\left(\frac{k\pi}{2m+1}\right) = m(2m+1)$
b) $\displaystyle \sum_{k=1}^{n-1}\tan^{2}\frac{k \pi}{2n} = \frac{(n-1)(2n-1)}{3}$
a) $\displaystyle \sum_{k=1}^{m} \tan^2\left(\frac{k\pi}{2m+1}\right) = m(2m+1)$
b) $\displaystyle \sum_{k=1}^{n-1}\tan^{2}\frac{k \pi}{2n} = \frac{(n-1)(2n-1)}{3}$