Question Number 166515 by greogoury55 last updated on 21/Feb/22
$$\:\:\:\:{Given}\:{a}\:{function}\: \\ $$$$\:\:\:\left({x}+\mathrm{1}\right){f}\left(−{x}\right)+\frac{\mathrm{1}−{x}}{\mathrm{4}{x}}\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{100}\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{{x}} \\ $$$$\:{x}\neq\mathrm{0}\:,\:{x}\neq\mathrm{1} \\ $$$$\:{Find}\:{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+...+{f}\left(\mathrm{400}\right) \\ $$
Answered by nurtani last updated on 21/Feb/22
$${f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+...+{f}\left(\mathrm{400}\right)\:=\:\mathrm{399} \\ $$