let-f-t-n-1-1-n-ln-1-t-2-n-1-t-2-1-study-the-simple-and-uniform-convergence-of-f-n-2-study-the-continuity-of-f-3-prove-that-lim-t-f-t-ln-2-pi-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 36750 by prof Abdo imad last updated on 05/Jun/18

let f(t)=Σ_(n≥1) (−1)^n ln{1+ (t^2 /(n(1+t^2 )))} 1) study the simple and uniform convergence of Σ f_n 2)study the continuity of f 3) prove that lim_(t→+∞) f(t)=ln((2/π)) .

$${let}\:{f}\left({t}\right)=\sum_{{n}\geqslant\mathrm{1}} \:\left(−\mathrm{1}\right)^{{n}} {ln}\left\{\mathrm{1}+\:\frac{{t}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}\right\} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:\:{and}\:{uniform}\:{convergence} \\ $$$${of}\:\Sigma\:{f}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{continuity}\:{of}\:{f} \\ $$$$\left.\mathrm{3}\right)\:{prove}\:{that}\:{lim}_{{t}\rightarrow+\infty} \:{f}\left({t}\right)={ln}\left(\frac{\mathrm{2}}{\pi}\right)\:. \\ $$

Facebook Tweet Pin

let-f-t-n-1-1-n-ln-1-t-2-n-1-t-2-1-study-the-simple-and-uniform-convergence-of-f-n-2-study-the-continuity-of-f-3-prove-that-lim-t-f-t-ln-2-pi-

Leave a Reply Cancel reply