Question Number 125884 by Dwaipayan Shikari last updated on 14/Dec/20
$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\sqrt{\mathrm{5}}−\mathrm{2}\right)^{{n}} \begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}}{\left(\left(\mathrm{2}{n}+\mathrm{1}\right)\left(\left(\sqrt{\mathrm{5}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\right)^{{n}+\frac{\mathrm{1}}{\mathrm{2}}} +\left(\sqrt{\mathrm{5}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\right)^{{n}−\frac{\mathrm{1}}{\mathrm{2}}} \right)\right)} \\ $$