Monotonic & Bounded Sequences | Real Analysis | IIT JAM | CUET PG 2027 | Lec-1 | IFAS

Monotonic & Bounded Sequences | Real Analysis | IIT JAM | CUET PG 2027 | Lec-1 | IFAS explained with clear concepts and exam-focused approach. Covers monotonic sequences, bounded sequences, real analysis PYQ tricks for IIT JAM, CUET PG. Clear problem-solving and shortcuts included.

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⏳ Lecture Timeline:
[00:00:00] – Introduction to Monotonic & Bounded Sequence
[00:05:02] – Definition: Sequence as Function
[00:10:22] – Notation & Basic Examples
[00:15:29] – Concept: Range of a Sequence
[00:20:05] – Important: Range Always Countable
[00:23:28] – Bounded Sequence Definition
[00:24:48] – Example: Unbounded (a_n = n)
[00:26:04] – Example: Bounded (1/n)
[00:27:23] – Bounded Below / Above Definitions
[00:33:29] – Question 1: Supremum of sin(π/n)
[00:36:24] – Trick: Finite Range ⇒ Bounded
[00:39:46] – Monotonic Sequence Definitions
[00:41:01] – Eventually Monotonic Concept
[00:42:44] – Question 2: Monotonicity of n²/2ⁿ
[00:48:07] – Question 3: Recursive Bounded Sequence
[00:52:43] – Trick: Difference of Bounded Sequences
[00:54:52] – Counterexample: Not Convergent/Monotonic
[00:55:26] – Homework: Practice Questions
[00:56:47] – Complete Session (Monotonic & Bounded Sequence)

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📖 Topics Covered in This Lecture:
• Sequence Definition, Notation & Range
• Bounded Sequence & Bounded Above/Below
• Monotonic Increasing/Decreasing Concepts
• Eventually Monotonic Sequences
• PYQ-based Problems & Short Tricks

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📚 Lecture Summary:
In this session, IFAS Expert Faculty focuses on monotonic and bounded sequences, explaining sequence definitions, range, boundedness, and monotonicity (increasing, decreasing, eventually monotonic). Key examples like sin(π/n), n²/2ⁿ, and recursive sequences are solved with PYQ-based tricks, reinforcing real analysis concepts for JAM and CUET PG exams.

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🎓 This lecture is highly beneficial for students preparing for:
✅ IIT JAM Mathematics
✅ CUET PG Mathematics
✅ TIFR Mathematics
✅ NBHM Mathematics

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🌟IIT JAM 2024: Total Selections: 800+ (AIR 1, 2, 3, 4, 8, 10...) 
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📄 View IFAS Result Sheet:
👉 https://drive.google.com/file/d/1THh6TuLtCuSyAYczcHygIV22F87jD238/view

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