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Question Number 166515 by greogoury55 last updated on 21/Feb/22

    Given a function      (x+1)f(−x)+((1−x)/(4x)) f((1/x))=((100(x^2 +4))/x)   x≠0 , x≠1   Find f(2)+f(3)+f(4)+...+f(400)

$$\:\:\:\:{Given}\:{a}\:{function}\: \\ $$$$\:\:\:\left({x}+\mathrm{1}\right){f}\left(−{x}\right)+\frac{\mathrm{1}−{x}}{\mathrm{4}{x}}\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{\mathrm{100}\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{{x}} \\ $$$$\:{x}\neq\mathrm{0}\:,\:{x}\neq\mathrm{1} \\ $$$$\:{Find}\:{f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+...+{f}\left(\mathrm{400}\right) \\ $$

Answered by nurtani last updated on 21/Feb/22

f(2)+f(3)+f(4)+...+f(400) = 399

$${f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{4}\right)+...+{f}\left(\mathrm{400}\right)\:=\:\mathrm{399} \\ $$

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