Rojas Bob
08/22/2023 · Elementary School
Soit \( \left(u_{n}\right) \) la suite définie pour tout \( n \in \mathbb{N} \) par: \( \quad u_{n}=3 n-4 \sin (n) \). 1. CalcularRice Afficher les 30 premiers termes de la suite sur le tableur de la calculatrice. Quelle conjec- ture peut-on émettre sur le comportement de la suite ( \( \left.u_{n}\right) \) lorsque \( n \) tend vers \( +\infty \) ? 2. Justifier que \( u_{n} \geqslant 3 n-4 \) pour tout \( n \in \mathbb{N} \). 3. En déduire la limite de la suite \( \left(u_{n}\right) \). 62
UpStudy ThothAI Solution
Tutor-Verified Answer
Quick Answer
1. Les 30 premiers termes de la suite \( (u_n) \) montrent une croissance linéaire. On peut conjecturer que \( \lim_{n \to +\infty} u_n = +\infty \).
2. On justifie que \( u_n \geq 3n - 4 \) pour tout \( n \in \mathbb{N} \) en montrant que \( \sin(n) \leq 1 \).
3. La limite de la suite \( (u_n) \) est \( +\infty \) car \( 3n \) domine \( -4\sin(n) \) lorsque \( n \) tend vers \( +\infty \).
Step-by-step Solution
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text
Enter your question here…
By image
Re-Upload
Submit