Soit fn(x) = (1)/(n + n3x) pour x R^+. Montrer que la série sum fn(x) converge simplement sur R^+.

May 18, 2026Mathematics

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May 18, 2026

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\frac{1}{n + n^3x} $pour$ x \in \mathbb{R}^+$.

Welcome back — been a while! Let's pick up where you left off.

Voici la solution de l'exercice 2.

On considère la série de fonctions $f_n(x) = \frac{1}{n + n^3x}$ pour $x \in \mathbb{R}^+$ .

1. Montrer que la série $\sum f_n(x)$ converge simplement sur $\mathbb{R}^+$

Step 1: Pour montrer la convergence simple, on fixe $x \in \mathbb{R}^+$ . Pour tout $n \ge 1$ et $x > 0$ , on a $n + n^3x > n^3x$ . Donc, $0 < f_n(x)

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Welcome back — been a while! Let's pick up where you left off. Voici la solution de l'exercice 2.

Asked on May 18, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 18, 2026

Welcome back — been a while! Let's pick up where you left off. Voici la solution de l'exercice 2. On considère la série de fonctions f_n(x) = (1)/(n + n^3x) pour x R^+. 1. Montrer que la série f_n(x) converge simplement sur R^+ Step 1: Pour montrer la convergence simple, on fixe x R^+. Pour tout n 1 et x > 0, on a n + n^3x > n^3x. Donc, $0 < f_n(x)