#17|Convergence of the sequence a_n=(1+1/n)^n| Applications of Monotone Convergence Theorem. скачать в хорошем качестве

#17|Convergence of the sequence a_n=(1+1/n)^n| Applications of Monotone Convergence Theorem.

In this lecture, we study the convergence of the famous sequence a_n = (1 + {1}/{n})^n, which plays a key role in the definition of the mathematical constant e. 📖 Topics Covered in this Video: ✔ Proof that the sequence is monotonic increasing ✔ Proof that the sequence is bounded above ✔ Application of the Monotone Convergence Theorem ✔ Result: \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e \approx 2.718 Show that lim n tends to infinity (1 + {1}/{n})^n = e approximately equal to 2.718 This concept is very important for B.Sc. 1st Semester Mathematics students and also for higher studies in Real Analysis, Calculus, and Competitive Exams (CSIR NET, GATE, IIT JAM, etc.). 🔔 Subscribe to Maths Lover for more detailed lectures on Sequences, Series, and Real Analysis. --- 📌 Hashtags: #ConvergenceOfSequence #MonotoneConvergenceTheorem #LimitOfSequence #Mathematics #BScMathematics #MathsLover #RealAnalysis #ExponentialConstant #CSIRNET #GATE #IITJAM #BSc1stSemester