Question Number 149155 by gsk2684 last updated on 03/Aug/21
$${find}\:{the}\:{coefficient}\:{of}\:{x}^{\mathrm{50}} \:{in}\:{the}\: \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{1000}} +\mathrm{2}{x}\left(\mathrm{1}+{x}\right)^{\mathrm{999}} +\mathrm{3}{x}^{\mathrm{2}} \left(\mathrm{1}+{x}\right)^{\mathrm{998}} +...\infty\: \\ $$