How to find the radius and interval of convergence of a power series

We will find the radius of convergence and the interval of convergence of the power series of n/4^n*(x-3)^(2n),

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[CycloneSlayer]

dude i watched like 25 mins of a calculus lecture and u explained it to me in 6, thank you

[peterheile]

Bro all of your videos are amazing. I don't know why but it just clicks with your explanations. Thank you.

[luna]

Just something to note: at 2:50 you make the analogy to complex analysis to why it's a "radius of convergence." I'd be careful! The more natural generalization, to me at least, is just to functions of several variables. If you have a function f(x, y) and you're doing its Taylor expansion, you'll get a circle as a radius of convergence in the x-y plane. If you have a function f(x1, x2, ..., xn), you'll get an n-ball as your radius of convergence. Taylor's theorem usually isn't taught in calc 3 for several variable functions but it's very useful!

[deko]

isn't it should to be ( n+1 / n ) ? cuz i have seen this before

[Vladimir_Pavlov]

You can also find the sum of the series in the convergence domain:
S=z/(1-z)^2, where z=(1/4) *(x-3)^2

[majwin-]

How do we know. When to use the. Root test and not the ratio

[lilstanni]

1:38 isnt the limit 1? sqrt of 1 is 1.
How did u get 4 insited.
Limit as n approach infinity sqrt ( (n * 4)/(n+1) ) This the same as sqrt ( 1 * 4/n) / (1 + 1/n)
If u take lim as infinity u get 1

[abhaypandey]

4:18, we know that 1+2+3+... converges to -1/12 ramanujan😢

[egbdf]

You've probably already gotten this comment a million times but Where'd you get the pokeball mic from

[foolart]

IT ALL MAKES SENSE NOWWW, im from romania and i was struggling to understand how i get the interval NOWW IT MAKES SENSEEE thank you sm

[PhillipYan-ykqd]

poor explnation, u skipped steps that made it hard for me to understand your thinking process, please do

[majwin-]

How do we know. When to use the. Root test and not the ratio