Embark on a comprehensive mathematical journey through the world of power sums in this 50-minute masterclass video. Explore millennia of mathematical discoveries, starting from basic principles and progressing to advanced techniques for summing quadrillions of powers by hand. Delve into a plethora of power sum formulas, witness captivating "proofs without words" animations, and unravel the mysteries of Bernoulli numbers. Gain a deep understanding of the Euler-Maclaurin summation formula through an accessible introduction. Challenge yourself with exercises on summation limit adjustments and discover the historical context behind Gauss's famous childhood sum. From the classic sum of 1 to 100 to complex algebraic manipulations and pattern recognition, master the art of power sums and their applications in mathematical problem-solving.