Mathematics - Complex Number Question with Solution | TestHub

If $Z_n=\left(\cos \left(\frac{\pi }{n(n+1)(n+2)}\right)+i\sin \left(\frac{\pi }{n(n+1)(n+2)}\right)\right)$ for $n=1,2,3\dots$ and the principle argument value of $\mathrm{z}={\lim }_{\mathrm{n}\to \infty }\left({\mathrm{z}}_1{\mathrm{z}}_2\dots \dots {\mathrm{z}}_{\mathrm{n}}\right)$ is $\frac{\mathrm{k}\pi }{24}$, then find the value of k