Real Analysis Full Course I Lec-5 I Sequence: Introduction I Free Notes I Hin-Eng

This is the lecture 5 of full length real analysis course for both iit-jam and csir-net. The topic is about Sequence: Introduction
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The topics to be covered here are,
Sequence: Both Bounded and Unbounded Sequences with examples
Convergent Sequence: Sandwich Theorem
Important Limits: (𝐥𝐢𝐦)┬(𝒏→∞ )⁡〖𝒙^(𝟏/𝒏)=𝟏〗, (𝐥𝐢𝐦)┬(𝒏→∞)⁡〖𝒏^(𝟏/𝒏)=𝟏〗, (𝐥𝐢𝐦)┬(𝒏→∞)⁡〖(𝟏+𝟏/𝒏)^𝒏=𝒆〗
Ratio Test: ( 𝐥𝐢𝐦 )┬( 𝒏→∞) 𝒏!/𝒏^𝒏 =?
Monotone Convergence Theorem