let-f-n-x-nx-2-e-x-n-x-0-1-study-the-simple-convergence-of-f-n-x-2-study-the-uniform-convergence-of-f-n-x-

Question Number 33347 by caravan msup abdo. last updated on 14/Apr/18

let f_n (x)= nx^2 e^(−x(√n)) , x≥0 1)study the simple convergence of Σ f_n (x{ 2) study the uniform convergence of Σ f_n (x).

$${let}\:{f}_{{n}} \left({x}\right)=\:{nx}^{\mathrm{2}} \:{e}^{−{x}\sqrt{{n}}} \:\:\:,\:{x}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right){study}\:{the}\:{simple}\:{convergence}\:{of} \\ $$$$\Sigma\:{f}_{{n}} \left({x}\left\{\right.\right. \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{uniform}\:{convergence}\:{of} \\ $$$$\Sigma\:{f}_{{n}} \left({x}\right). \\ $$

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