Infinite Series | Convergence of Series | P-Series Test | Real Analysis-I | B.Sc. 1st Year

Infinite Series | Convergence of Series | P-Series Test | Real Analysis-I | B.Sc. 1st Year Welcome to K.Mathematics! In this lecture of Real Analysis-I, we study one of the most important topics for B.Sc. 1st Year Mathematics—Infinite Series. In this video, you will learn the fundamentals of infinite series, convergence of series, Cauchy Criterion, the nth Term Test, convergence of positive term series, and the P-Series Test with detailed explanations and solved examples. The lecture is designed according to the B.Sc. Mathematics syllabus and is useful for university semester examinations as well as competitive exams such as CSIR-NET, GATE, JAM, CUET (PG), SET, and other M.Sc. entrance examinations. 📌 Topics Covered ✔️ Introduction to Infinite Series ✔️ Partial Sums of a Series ✔️ Convergence and Divergence of Series ✔️ Geometric Series ✔️ Cauchy Criterion for Series ✔️ nth Term Test ✔️ Convergence of Positive Term Series ✔️ P-Series Test ✔️ Solved University-Level Problems ⏱️ Video Chapters 00:00 – Introduction 00:45 – Infinite Series 04:12 – Convergence of Series 15:31 – Cauchy Criterion for Series 17:09 – nth Term Test 19:52 – Convergence of Positive Term Series 30:05 – Solved Problems 🎯 This Lecture is Helpful For • B.Sc. 1st Year Mathematics Students • Utkal University • Fakir Mohan University • Ravenshaw University • Sambalpur University • Berhampur University • North Odisha University • Other Indian Universities following similar Real Analysis-I syllabi • CSIR-NET Mathematical Sciences • IIT JAM Mathematics • GATE Mathematics • M.Sc. Mathematics Entrance Examinations 📖 Suggested Previous Lecture 🔹 Sequences of Real Numbers 🔹 Monotone Sequences 🔹 Bounded Sequences 🔹 Limit of a Sequence 🔹 Monotone Convergence Theorem 🔔 If this lecture helped you 👍 Like the video 💬 Comment your doubts below 📢 Share it with your classmates ❤️ Subscribe to K.Mathematics for complete B.Sc. Mathematics courses, university exam preparation, and competitive mathematics. 📌 Keywords Infinite Series, Convergence of Series, Divergence of Series, Partial Sums, Sequence of Partial Sums, Cauchy Criterion for Series, nth Term Test, Positive Term Series, P-Series Test, Geometric Series, Telescoping Series, Real Analysis, Real Analysis-I, B.Sc Mathematics, B.Sc 1st Year Mathematics, Mathematical Analysis, University Mathematics, Infinite Sum, Convergence Tests, Mathematics Lecture, K.Mathematics, CSIR NET Mathematics, IIT JAM Mathematics, GATE Mathematics, UGC NET Mathematics, Semester 1 Mathematics, Real Analysis Notes, Infinite Series Problems. #️⃣ Hashtags #InfiniteSeries #RealAnalysis #BScMathematics #Mathematics #PSeries #ConvergenceOfSeries #CauchyCriterion #NthTermTest #GeometricSeries #KMathematics #RealAnalysisI #UniversityMathematics #CSIRNET #IITJAM #GATEMathematics