Alternating Series | Alternating Series Test (Leibniz Test) | Real Analysis-I | B.Sc. 1st Year

Alternating Series | Alternating Series Test (Leibniz Test) | Real Analysis-I | B.Sc. 1st Year Welcome to K.Mathematics! In this lecture, we study one of the most important topics in Real Analysis-I—the Alternating Series and the Alternating Series Test (Leibniz Test). This topic forms the foundation for understanding conditional convergence and is essential for B.Sc. 1st Year Mathematics, University Semester Examinations, CSIR-NET, IIT JAM, GATE Mathematics, and other competitive examinations. In this video, you will learn what an alternating series is, the mathematical definition of an alternating sequence, the statement and proof of the Leibniz Test, the conditions under which it can be applied, and how to determine whether an alternating series converges. The lecture also includes several solved university-level problems explained step by step. Whether you are preparing for your semester examinations or strengthening your Real Analysis concepts, this lecture will help you build a solid understanding of alternating series and conditional convergence. ⏱️ Time Stamps 00:00 – Introduction 00:50 – Alternating Series: Definition & Examples 05:32 – Alternating Series Test (Leibniz Test): Statement & Proof 11:35 – Solved Problems 📚 Topics Covered Alternating Sequence Alternating Series Mathematical Definition Examples of Alternating Series Alternating Series Test (Leibniz Test) Conditions of the Leibniz Test Proof of the Alternating Series Test Convergence of Alternating Series Conditional Convergence Absolute vs Conditional Convergence University-Level Solved Problems Examination Tips 🎯 This Video is Useful For B.Sc. 1st Year Mathematics Students Utkal University Fakir Mohan University Sambalpur University Berhampur University Ravenshaw University Odisha State Universities CSIR-NET Mathematical Sciences IIT JAM Mathematics GATE Mathematics M.Sc. Mathematics Entrance Examinations If you find this lecture helpful, please Like, Share, and Subscribe to K.Mathematics for more high-quality lectures on Real Analysis, Calculus, Linear Algebra, Abstract Algebra, Differential Equations, and Competitive Mathematics. 🔔 Don't forget to press the Bell Icon so you never miss upcoming mathematics lectures. #realanalysis #alternatingseries #leibniztest #conditionalconvergence #realanalysis1 #bscmathematics #bsc1styear #mathematics #analysis #infiniteSeries #kmathematics #csirnet #gateMathematics #iitjam #utkaluniversity #odisha #mathlecture #highermathematics