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so waht is your question?
Find the radius of convergence and the interval of convergence of the power series. the sum from n=0 to infinity of 2^n x^n / n!
so i used ratio test and found it converges absolutely, but im not sure how to find the Radius on convergence or interval
Do you mind giving me the last few lines of your ratio test?
well it boiled down to lim=|2x/n+1|
COOL i got that too
so limn->inifinity, 2x/(n+1) -> 0
that mean the interval is (-infin, infin) and radius of convergence is infinity
ok, just so i understand though what is the R value
oh is it infinity
so how was i able to decipher that the R value is infinity just from knowing the series converged absolutely?
i guess im asking why does geting L=0 from the ratio test help me
u can interpret it this way lim n->infin |x|(2/(n+1))<1 , then |x|<1/ 0 |x|
X is a constant. So no mater what X is, the limit will go to 0, and the ratio test states that if the limit is <1, it converges. So X can be any real numbers
ah ok, so becasue this series converges no matter what x-value is plugged in: my x value can range from -infinity to +infinity bc it will always converge. and then the radius for that interval is infinity also
YEP that is it!!
thankyou very much i appreciate it. and just for learning purposes, do i know this series is centered at 0?
and that is bc the x-a isnt there?
Becasue it is the form of c0+c1(x)+c2(x)^2 +....cn(x)^n
so its in the c0 form
i think i get this
yea cn(x)^n then it is centered at 0, if it is cn(x-1)^n then it would be centered at x=1
and in my equation here the 2^2/n! is the Cn part
u got it?
right right ok im dumb
LOL no i know that is you meant.
2^2 is just a typo~~
yup my fault
well i really do appreciate this. It may not seem it but you just helped someone who will most likely be getting early admission to UB med school ha ha Ive been getting pounded with organic and inorganic so this has been on the back burner
LOL my pleasure and honor :P
keep up the good work you are really patient, and a good listener. Guys like you are doing it for the love of the game if you will.
LOL alright if u have any further questions, just post here :) i am gonna go now Bye :)
oh can you find the radius of convergence for this power series : sum n = 0 to n =infinity ((x+3)^n)/(e^3n!)
welp i think the ratio test gives you the limit to approach zero again, so i guess its infinity again?
Thanks lol i was arguing with my friend about the convergence of this series.
yeah like at the end of my ratio test i got x+3 ontop
but the numerator is like e^3n+1 time e^3n+2 times e^3m+3 so thats infinity
i just meant denominator* sorry so basicall that makes the denom infinity and the numerator x+3
yea haha Thanks!~