Geometric Series

Geometric series. In this video, I prove the formula for the geometric series, which is the most important example of a series. It is used many times in calculus and is the basis of Zeno's paradox. Enjoy the math adventure!

[abhilashsaha]

Exactly what I needed for next week's test. Thank you, Dr Peyam.

[juanmolinas]

Greetings Doctor!, How well do you explain, I am Spanish-speaking and I still understand him reasonably well

[خالدالحماديالحمادي-به]

Wow thank you, it was so useful for me 👏🏻

[GhostyOcean]

The way that I discovered these two formulas was to do it the other way! I found S = 1+r+r²+… =1/(1-r), and used this to find the partial sum formula with a little manipulation. Proof that that's actually the partial sum uses induction, but finding the formulas is nice in either method!

[isobar]

At last one I can follow...and understand! Thanks professor. Now if you can derive the Euler/ Lagrange calculus of variations from first principles, I would be most grateful...I can never quite get my head around it.

[rikhalder]

Please tell me why magnitude of a vector is written by modulus. But it should be represented by norm.

[musik]

Shouldn't we also exclude r=0, as that would lead to the assumption 0^0 = 1?

[Galileopi]

I knew it, but it is always good to remember these sorts of properties. When do you explain tensors, Laplace transformation, Reiman surfaces, and so on?. Share knowledge is our duty and pleasure.

[AshishSingh-]

What is a difference between AP and Gp