soit la serie de fonction Σ_(n=2 ) (x^n /(nx+ln(n))) etudie la convergence simple sur [0,1[


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Question Number 165240 by SANOGO last updated on 28/Jan/22

$s o i t l a s e r i e d e f o n c t i o n \sum_{n = 2} \frac{x^{n}}{n x + l n (n)}$ $e t u d i e l a c o n v e r g e n c e s i m p l e s u r [0, 1 [$
	Answered by mindispower last updated on 28/Jan/22

	$\forall a \in [0, 1]$ $0 ⩽ \sum_{n ⩾ 2} \frac{a^{n}}{n a + l n (n)} ⩽ \sum_{n ⩾ 2} \frac{a^{n}}{l n (2)}$ $\sum_{n ⩾ 2} \frac{a^{n}}{l n (2)} . c v \forall a \in [0, 1 [$ $\Rightarrow \sum_{n ⩾ 2} \frac{x^{n}}{n x + l n (2)} C v$
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