Root Test for Series

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May 18, 2013
neggsa Says:
Patrick I love you! Your videos have helped me so much throughout calc 1 and now calc 2! Thank you for making these videos, so many of us appreciate it!!

May 5, 2013
Miguel Zeng Says:
you are right, strawberry, Patrick just messed up his wording. he meant 1/n approaches 0 and since 1/n is the exponent, it means that the value of the power becomes 1 and then 1 * 3^3

Apr 26, 2013
199alexman Says:
you're welcome. i checked it on wolfarmalpha. c o m it goes to infinity.

Apr 25, 2013
4everstrawberryhills Says:
haha thanks. That wouldn't work because you have to divide by the largest variable that's found in the denominator, and there's no variable present in the denominator in this case. So that method wouldn't work. Also, I just double-checked the limit for this series on a computational website and it is intact infinity, Patrick is right. Sorry!

Apr 24, 2013
199alexman Says:
first i would like to say you have nice picture, second is so if you change n in terms of X then divide all numerator and denominator by x then you know the rules from there in top u will get x/x which is one down you divide 3/x which is zero time 3^1/x is zero so u will get 1/0 !

Apr 22, 2013
4everstrawberryhills Says:
Actually no, because 3^(1/n) gives you 3^(1/inf) (when taking the limit) so you get 3^0, which is 1. 3^3 is 27, so 27*1=27.

Apr 20, 2013
smatrick0208 Says:
you sound like the hippie teacher on beavis and butthead. On a serious note your videos are very helpful. Thank you for posting!

Apr 16, 2013
teeman9266 Says:
Im wondering the same thing, i asked my instructor today and he refused to say anything but review my note. I dont remember learning anything about why 1 + 1/x = e

Apr 15, 2013
Mr6fraan Says:
you better add great and powerful for the p-test and geometric test lol

Apr 12, 2013
HarshadKeLiye Says:
I'm just a bit confused about WHY you cannot do that :/

Mar 22, 2013
NarutorRasengan Says:
That is not quite right. While it's true that 1/infinity goes to zero, 3^(1/n) would go to 1. Recall that anything with an exponent of 0 becomes 1. What you were looking at was only the 1/n, you forgot that the 3 was raised to the power of 1/n.

Mar 21, 2013
1234livelifelove Says:
can somebody please explain how you get the 'e' at the last part? i dont quite get it. Greatly appreciate! <3

Mar 20, 2013
sebastianzx6r Says:
Are you talking about the part: n/(3^1/n *3^3)? If you look at 3^1/n as n goes to infinity, it becomes 3^(1/infinity). That equals 3^0, remember this equals 1. Your denominator just becomes 1*27

Mar 20, 2013
sebastianzx6r Says:
1^infinitiy means you go 1X1X1X1X1.. infinity many times. 1 times itself will never grow right? So it stays at 1. If it was any number >1^infinity,then yes it would be infinity.

Mar 20, 2013
sebastianzx6r Says:
Ratio test is usually when you have factorials and exponential stuff. Yes all this stuff is raised to the n^2, but if you threw in n+1 for all the n's, simplifying it would be a nightmare. Whenever you see an entire series raised to n, it's best to use the root test because you will eliminate the n or reduce it's power like in the example this dude did.

Mar 17, 2013
199alexman Says:
you have mistake in 5:45 as you wrote 3^91/n . 3^3 the first term will go to 0 and times 27 is zero so its actually is infinity over zero! right...

Mar 5, 2013
Jade Rong Says:
Why is it e??

Feb 11, 2013
Johnny Do Says:
I love seeing all of the steps. Thanks!

Feb 6, 2013
brisingrsword01 Says:
How does this differ from the ratio test?

Video Details

Questions with Detailed Solutions about Sequences and Series made by me! http://www.teacherspayteachers.com/Product/Ca
lculus-Sequence-and-Series-Questions-with-Sol
utions Root Test for Series - Using the Root Test to Determine if a Series Converges or Diverges! The test along with 3 full examples ... More