How to evaluate a series with the Riemann zeta function

Do you think finding the sum of an infinite series interesting? If so, you can learn more from Brilliant https://brilliant.org/blackpenredpen/ (20% off with this link) We will find the series of zeta(s)-1 and it turns out to be a double summation problem. See here for another example of changing the order of a double summation: https://youtu.be/8BGxSgSkc2c. We will end up with a geometric series and then a telescoping series! Note, the limit of zeta(s) as s goes to infinity is tricky. Be sure to do it carefully. 💪 Support this channel and get my math notes by becoming a patron: https://www.patreon.com/blackpenredpen 🛍 Shop my math t-shirt & hoodies: https://amzn.to/3qBeuw6 ---------------------------------------- #blackpenredpen #math #calculus #apcalculus Riemann Zeta t-shirt: 👉 https://bit.ly/zetatee 0:00 Quick intro to Riemann Zeta function and its special values 3:20 Main question of the day: Series of zeta(s)-1 9:59 Check out Brilliant 10:55 bonus part (limit of the zeta function)