Real Analysis 04 | Sequence and Series of Functions in ONE SHOT

Time Stamps:
0:00:00 Introduction
0:06:00 Arbitrary Series
0:21:27 Rearrangement of Series
0:46:00 Sum of Series
0:54:27 Telescoping Series
1:06:22 Sequence of Functions
1:38:22 Series of Functions
1:57:00 Questions Practice

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[navneetmiradwal]

thankyou for the detailed and easy explaination

[tomatobasumatary]

Sir please finish the syllabus ☺️

Finite and infinite sets, examples of countable and uncountable sets. Real line, bounded sets,
suprema and infima, completeness property of R, Archimedean property of R, intervals.
Concept of cluster points and statement of Bolzano-Weierstrass theorem.
Real Sequence, Bounded sequence, Cauchy convergence criterion for sequences. Cauchy’s
theorem on limits, order preservation and squeeze theorem, monotone sequences and their
convergence (monotone convergence theorem without proof).
Infinite series. Cauchy convergence criterion for series, positive term series, geometric series,
comparison test, convergence of p-series, Root test, Ratio test, alternating series, Leibnitz’s test
(Tests of Convergence without proof). Definition and examples of absolute and conditional
convergence.
Sequences and series of functions, Point wise and uniform convergence. Mn-test, M-test,
Statements of the results about uniform convergence and integrability and differentiability of
functions, Power series and radius of convergence.