Integral Test Derivation amp 1st Example

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The Integral Test is a beautiful piece of mathematics that relates an infinite series to an improper integral. Both get interpreted geometrically, and this results in the fact that the corresponding improper integral converges or diverges precisely when the series converges or diverges. This is particularly useful when we have a complicated series we don't understand, but the corresponding function is one we know how to integrate. However, this is also the source of its main limitation: if we can't integrate the function, it just isn't helpful. • **************************************************** • YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems! • **************************************************** • ►Full Course Playlist: CALCULUS II: • Calculus II (Integration Methods, Ser... • **************************************************** • Other Course Playlists: • ►CALCULUS I: • Calculus I (Limits, Derivative, Integ... • ►DISCRETE MATH: • Discrete Math (Full Course: Sets, Log... • ►LINEAR ALGEBRA: • Linear Algebra (Full Course) • *************************************************** • ► Want to learn math effectively? Check out my Learning Math Series: • • 5 Tips To Make Math Practice Problems... • • ►Want some cool math? Check out my Cool Math Series: • • Cool Math Series • ***************************************************** • ►Check out my 2nd Channel for lower production quality live math videos: / @drtreforuvic • ***************************************************** • ►Follow me on Twitter: / treforbazett • ***************************************************** • This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. • BECOME A MEMBER: • ►Join: / @drtrefor • MATH BOOKS MERCH I LOVE: • ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett

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