Limit of a Sequence | Real Analysis | CSIR NET Mathematics | Lec 08 | IFAS скачать в хорошем качестве

Limit of a Sequence | Real Analysis | CSIR NET Mathematics | Lec 08 | IFAS

In this lecture by IFAS, Manoj Sir explains the concept of the Limit of a Sequence with a focus on problem-solving for competitive exams. This session is part of the Emotion 2.0 series, designed for CSIR NET Mathematical Science, GATE, and SET aspirants to build a solid foundation in Real Analysis through high-yield questions and detailed logical reasoning. 🔥 Join India's Best Mathematics Coaching for CSIR NET and GATE Exams Live Online Course & Recorded Course - https://ifasonline.com/ 👉🏻IFAS CSIR UGC NET Mathematical Science Result👈🏻: CSIR - NET June 2025 - Total Selections: 4200+ (CSIR UGC JRF AIR 1, 2, 6, 6, 10.....) CSIR - NET Dec 2024 - Total Selections: 4000+ (CSIR UGC JRF AIR 5, 6, 6, 7, 8, 9, 10......) CSIR - NET June 2024 - Total Selections: 2000+ (CSIR UCG JRF AIR 3, 10, 13, 15, 16.....) CSIR - NET Dec - 2023: Total Selections: 1200+ (CSIR UGC JRF AIR 2, 4, 5, 7, 12, 15, 18, 19......) CSIR - NET June - 2023: Total Selections: 1000+ (CSIR UGC JRF AIR 2, 6, 8, 9.....) ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🎯 Target Audience: This video is highly beneficial for students preparing for: CSIR NET Mathematics, GATE Mathematics, MH SET Mathematics, BARC, NBHM ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 👇 Watch the Full Lecture to Master These Topics: Sufficient Conditions for Convergence Counter-Examples in Sequences Ratio Test for Sequences Monotonic Sequence Theorem Complementary Subsequences Bolzano-Weierstrass Theorem Limit Superior and Limit Inferio ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ ⏱️ Timestamps - Jump to Your Topic: [04:18] Introduction to Limit of a Sequence and Session Agenda [05:57] Problem 1: Sufficient Conditions for Sequence Convergence [15:10] Problem 2: Analyzing $a_n = (1 + 1/n)^n$ (Boundedness and Monotonicity) [18:52] Problem 3: Applying Ratio Test and Series Convergence to Sequence Limits [22:09] Problem 4: Complementary Subsequences (Even vs. Odd Terms) [27:49] Discussion: Difference between Necessary and Sufficient Conditions [33:01] Problem 5: Bounded Sequences and Unique Limit Points [35:53] Problem 6: Unbounded Sequences and Divergent Subsequences [48:13] Problem 7: Always True Statements (Monotonicity & Boundedness) [49:17] Problem 8: Convergence of Monotonic Sequences with Convergent Subsequences [56:23] Identifying False Statements in Sequence Theory [01:06:50] Problem Solving: Multiple Conditions for Convergence (MSQ Practice) ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Lecture Summary: In this session, Manoj Sir focuses on Limit of a Sequence Mixed Examples, bridging the gap between theoretical definitions and exam-style applications. The lecture covers essential results like the Monotonic Convergence Theorem and the Sequential Criteria for limits. Beyond mathematical content, Manoj Sir shares insights into the mindset required for CSIR NET preparation, emphasizing the importance of identifying logical fallacies. The session concludes with a transition towards preparing for upcoming mock tests and specialized batches. ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🔗 Important Links: 🌍 Visit our Website: https://ifasonline.com 📞 Contact for Queries: 9172266888 📲 WhatsApp: https: https://whatsapp.com/channel/0029VbCV... 🔥 Qualification Prediction (Free Tool): https://ifasonline.com/QualificationP... 📘 Get Detailed Free Counselling: https://ifasonline.com/csir-net/mathe... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ Download IFAS: 👇 📲Android: https://play.google.com/store/apps/de... 📲 Ios: https://apps.apple.com/us/app/ifas/id... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ CSIR NET Mathematical Science Live & Recorded Course – https://ifasonline.com/csir-net/mathe... GATE Mathematical Science Recorded Course – https://ifasonline.com/gate/mathemati... MH SET Mathematical Science Recorded Course – https://ifasonline.com/mh-set/mathema.... 📘 Buy CSIR NET Mathematical Science Books: https://ifasonline.com/csir-net/mathe... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 📞 Contact for Admission: 9172266888 Stay Updated Via Other Social Media: ✔Telegram: https://t.me/NET_GATE_SET_Maths_Discu... ✔Instagram:   / csir_net_mathematical_science   ✔Facebook:   / ifasmaths   ✔WhatsApp: https: https://whatsapp.com/channel/0029VbCV... ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ #csirnetjune2026 #csirnetmaths #csirnetmathematics #csirnetmathematicalscience #csirnetpreparation #ifas