let f_n (x)= n^x e^(−nx) with x>0 1) study the simple and uniform convervence for Σ f_n (x) 2) let S(x)= Σ_(n=1) ^∞ f


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Question Number 33698 by math khazana by abdo last updated on 22/Apr/18

$l e t f_{n} (x) = n^{x} e^{- n x} w i t h x > 0$ $1) s t u d y t h e s i m p l e a n d u n i f o r m c o n v e r v e n c e f o r$ $Σ f_{n} (x)$ $2) l e t S (x) = \sum_{n = 1}^{\infty} f_{n} (x) . p r o v e t h a t$ $S (x) \sim \frac{1}{x} (x \to 0^{+})$
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