Math  /  Calculus

QuestionÉtudiez la convergence (absolue ou conditionnelle) de la série alternée : n=1(1)n(n7n2+3)\sum_{n=1}^{\infty}(-1)^{n}\left(\frac{n}{7 n^{2}+3}\right)

Studdy Solution
Vérifier que limnan=0\lim_{n \to \infty} a_n = 0 :
limnn7n2+3=limn17n+3n=0 \lim_{n \to \infty} \frac{n}{7n^2 + 3} = \lim_{n \to \infty} \frac{1}{7n + \frac{3}{n}} = 0
Toutes les conditions du test des séries alternées sont satisfaites.
La série converge conditionnellement.

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