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let-f-n-x-1-n-ln-1-x-2-n-1-x-2-and-f-x-f-n-x-find-lim-x-f-x-




Question Number 45961 by maxmathsup by imad last updated on 19/Oct/18
let f_n (x)=(−1)^n  ln(1+(x^2 /(n(1+x^2 )))) and f(x)=Σ f_n (x)  find lim_(x→+∞) f(x).
$${let}\:{f}_{{n}} \left({x}\right)=\left(−\mathrm{1}\right)^{{n}} \:{ln}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\right)\:{and}\:{f}\left({x}\right)=\Sigma\:{f}_{{n}} \left({x}\right) \\ $$$${find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$

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