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


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Question Number 36750 by prof Abdo imad last updated on 05/Jun/18
$let f(t)=Σ_(n≥1) (−1)^n ln{1+ (t^2 /(n(1+t^2 )))} 1) study the simple and uniform convergence of Σ f_n 2)study the continuity of f 3) prove that lim_(t→+∞) f(t)=ln((2/π)) .$
$l e t f (t) = \sum_{n ⩾ 1} {(- 1)}^{n} l n {1 + \frac{t^{2}}{n (1 + t^{2})}}$ $1) s t u d y t h e s i m p l e a n d u n i f o r m c o n v e r g e n c e$ $o f Σ f_{n}$ $2) s t u d y t h e c o n t i n u i t y o f f$ $3) p r o v e t h a t {l i m}_{t \to + \infty} f (t) = l n (\frac{2}{π}) .$
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