Remember that each term in the series {3, 7, 11, ...} adds 4 to the previous term, so the term before (4n-1) in the numerator is (4n-5). This term cancels with the (4n-5) in the denominator, leaving (4n-1) in the numerator.
Hey thanks for the video, helped a lot ! At 16:20 though, when finding the limit value at n = ∞ , I felt the factoring out of n was missing, and staying with n^(-1) so they zero off, and then 4/4 really is one. Someone could take that part too naively .. Thanks again you're great !
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction. So she is actually correct and the radius of convergence is in fact 1.
Hey did you forget about the 4n-5 in the denominator when solving for the radius of convergence? It seems to just disappear from your first line of multiplying the inverse to the second line where you are simplifying the factorial Thanks!
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction. So she is actually correct and the radius of convergence is in fact 1.
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction.
TH-cam got me feeling like a Pokémon Trainer. “Krista King, I choose you” (except I am being trained 😂) Krista King my organic chemistry tutor Khan academy Black pen red pen 3blue1brown Crashcourse Professor Dave MIT open You evoke them at different times.
+CalculusExpert.com You have one in 13:40 and it does make sense to put in the denominator because of the ratio test would multiply the reciprocal of the function An. You put it but later ignore it
Yes but you need to divide the n+1 equation by the regular n equation, meaning that the 4n-5 should be divided into (or multiply if you switch the fraction around) the new 4n-1 equation
integralCALC 14:10 what happend with (4n-5) in denominator? :S
o_o im confussed o_o
She must have forgot it!
Owww, she was right. The 4n-5 in the denominator cancels out the 4n-5 in the numerator (which was right before 4n-1)
Remember that each term in the series {3, 7, 11, ...} adds 4 to the previous term, so the term before (4n-1) in the numerator is (4n-5). This term cancels with the (4n-5) in the denominator, leaving (4n-1) in the numerator.
Thank you times a million seriously ! You're great and very very easy to understand ! Best explanation I've found so far
Aww thanks! :D
at 10:24 If you look at (1-x)^.25 in the upper left
look at the x term
|-x| < 1 = R
= |x| < 1 = R
It gives you R without a ratio test!
Hey thanks for the video, helped a lot ! At 16:20 though, when finding the limit value at n = ∞ , I felt the factoring out of n was missing, and staying with n^(-1) so they zero off, and then 4/4 really is one. Someone could take that part too naively .. Thanks again you're great !
You are a math genius Miss Crystal
14:10 what happend with (4n-5) in denominator? :S
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction. So she is actually correct and the radius of convergence is in fact 1.
Hey did you forget about the 4n-5 in the denominator when solving for the radius of convergence? It seems to just disappear from your first line of multiplying the inverse to the second line where you are simplifying the factorial
Thanks!
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction. So she is actually correct and the radius of convergence is in fact 1.
Very helpful and clear. I had a problem with a letter constant, this didn't help very much, but still allowed me to understand the process.
This tutorial helps explain a lot. Your a star thank you.
But where did the (4n-5) in the denominator disappear to?
Hi ma'am what happened to the (4n-5)?
wait... what happened to the (4n-5) term on the righthand side?
That is one of the things that she did not do a very good job of explaining, but if you think about what 3*7*11*...(4n-1) means, it basically states that all values that fit the pattern (+4 each time) up until (4n-1). The number in the sequence in the pattern directly before (4n-1) would then be 4 less, or 4n-5 which cancels with the 4n-5 on the bottom of the fraction.
What happened to (4n-5)?🤔
great dear ,u have a very clear voice , thank you so much
+Arun Kaparwan You're welcome!
Shouldn't the 11/4 be negative? (1/4-3)=-11/4, making that term positive? Thanks for uploading your videos, it's a lot of help!
Oh you're right! Great catch, thank you for letting me know so that I can fix it! :) And I'm so glad the videos are helpful! :D
What-th term is 3 y z^2 in the expansion of (x+y+z)^3 ? (3 second)
you explain it so easy! thank you so much
You're welcome, I'm glad it helped! :)
Krista the Queen math my question is for convergence the index of series must be negative...? ...can you explain it
hey.
could you help me here.
i have a series 3C1 +7C1+... (4n-1)Cn... how do i sum it up?
very very neat and clear
Hi thank you for your videos, can you provide more examples and reviews for calculus part 2 (integration, application of integrals, series etc)?
My calculus 2 playlist is a great place to start! th-cam.com/play/PLJ8OrXpbC-BPLux1qeQRT99STURIqtGrz.html
THanks for a reply, I hope your channel will become more popular!
great video! thanks for the help.
theHalleyMD You're welcome, glad I could help!
TH-cam got me feeling like a Pokémon Trainer. “Krista King, I choose you” (except I am being trained 😂)
Krista King
my organic chemistry tutor
Khan academy
Black pen red pen
3blue1brown
Crashcourse
Professor Dave
MIT open
You evoke them at different times.
very very helpful thank you
Thank you
What happend to (4n-5)? I see nowhere...
It became 4n-1 when we substituted n+1 for n.
thank you so much !!
+kyung baek You're so welcome!
Thank you. Now I knew ! :)
+cheridan hojas You're welcome!
Hey Krista, put this in your udemy calc 2 class, it is missing :D
Done! :)
You forgot the 4n-5 in the denominator! Then the limit would go to 0 and the radius would be infinity!
+BlueBunnyGamer There should have never been a 4n-5 in the denominator.
+CalculusExpert.com You have one in 13:40 and it does make sense to put in the denominator because of the ratio test would multiply the reciprocal of the function An. You put it but later ignore it
+BlueBunnyGamer The 4n-5 became 4n-1 because we had to substitute n+1 in for n, which changed 4n-5 to 4(n+1)-5, or 4n+4-5, or 4n-1.
Yes but you need to divide the n+1 equation by the regular n equation, meaning that the 4n-5 should be divided into (or multiply if you switch the fraction around) the new 4n-1 equation
I was wondering this as well...
great!
You should be my math tutor.....and wife :)
would have been easier to understand if you stated R = 1/L
I thought k had to be not a non negative