Could 1-1+1-1+1-1+1-1+... actually converge? скачать в хорошем качестве

Could 1-1+1-1+1-1+1-1+... actually converge?

Keep exploring at ► https://brilliant.org/TreforBazett. Get started for free for 30 days — and the first 200 people get 20% off an annual premium subscription! A series convergence in the normal sense when the limit of partial sums converge. We will commonly say the geometric series converges and the harmonic series diverges because their partial sums do. But Cesàro Summation instead considers the average of the partial sums and asks whether the limit of those converge. For example, 1-1+1-1+1-1... diverges in the normal sense, but because the average of its partial sums is 1/2, it converges in the Cesàro sense. A great example of this is with Fourier Series which experience big jumps near the discontinuities called Gibb's phenomenon. Taking Cesàro sums of the Fourier approximations (called Fejer Sums) instead smooths out Gibb's phenomenon. 0:00 Ordinary Convergence (Review) 3:04 Cesàro Summation 8:18 Fourier Series (Review) 9:28 Cesàro Summation improves Fourier Series 11:28 Brilliant.org/TreforBazett COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...   ► CALCULUS II:    • Calculus II (Integration Methods, Series, ...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems Actu...   ►Cool Math Series:    • Cool Math Series   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography