Limit Comparison Test and Direct Comparison Test

jarod5181991 Says:

Apr 11, 2012 - what about 20 of those questions under a 60 minute duress :P

svmgv Says:

Apr 11, 2012 - I love how you're trying not to ruin the surprise of the second example. Chortle.

svmgv Says:

Apr 11, 2012 - Not sure what we are looking for when doing either comparison test? Something that looks like a geometric or p-series?

BeeryGamer Says:

Apr 15, 2012 - Why is 3/n also smaller than 1?

username6333 Says:

Apr 15, 2012 - I am a little confused on that part as well but my guess would be: n is a really big number. Even if you include the 3/n which would be 3/n*2/n*1/n= 6/n^3 this is still a convergent p series, so the answer comes out to be the same.

wolde92 Says:

Apr 16, 2012 - you need to be in calc 0

SaluteTheRocker Says:

Apr 18, 2012 - Normally, you would multiply fractions. (1/2)*(1/2)=(1/4). However, the (1/2) is in the exponents. And when you do multiplication using exponents, you add the exponents. (1/2)+(1/2)=1. n^(1/2)*n^(1/2)=n^1, or just n.

Haxcz Says:

Apr 25, 2012 - When you multiply like bases, you add the exponents.1/2 + 1/2 = 1

MrLikeABaus Says:

Apr 25, 2012 - hmmm (1/2)+(1/2).. NOT (1/2)*(1/2)

superman3621 Says:

Apr 25, 2012 - thank you for all your help. ever since high school i've been watching you're videos and now I've passed my first year of math and i am finally FREE from it. thanks again!

StayClassyYou Says:

Apr 27, 2012 - For the geometric series you said: "1 to any power is 1" so 1/10^n = (1/10)^nI thought that 1^infinity was indeterminate. Is this not true? Or does it not matter somehow? Thanks for the videos, they're all excellent and very helpful. I'm just not clear on this part. Thanks.

Thunder7messiFan Says:

Apr 27, 2012 - Thanks Patrick! I've been watching your videos all semester and now they're great for reviewing for the final :)

AdamFidler1 Says:

Apr 27, 2012 - I would figure that if you multiply 1 by itself even an infinite amount of times you would still have 1. You could be right though, seemingly weird stuff can happen once you introduce infinity...

StayClassyYou Says:

Apr 27, 2012 - Intuitively what you're saying makes sense, but I was told in class that 1^infinity is indeterminate and a google search gave me the same answer. I can't find a good explanation why except that it has something to do with infinity not being a real number. I'm not sure if I would be able to use the example he showed in the video, or if there is some kind of exception, rule for determination, etc. Thanks though.

AnthonyPickett Says:

Apr 28, 2012 - lol. major fail dude. you add powers. good try though

ELop3d Says:

Apr 30, 2012 - I understand how sin(n) is always -1 < sin(n) < 1 .... so I thought it turned into (-1)^n. How do you simply come up with 2 / 10^n as your b-sub-n? Would you mind being at least slightly detailed? I'm just a little confused. Thank you in advance. I hope you have the time to respond. Your videos are excellent and I am extremely appreciative of the work you do.

ELop3d Says:

Apr 30, 2012 - Also, 1 other question. How did you conclude the 2 / n^2 in the next problem? I see how you got it, but why are you able to do that? Is there another (better) series test to tackle this problem with? It's just hard for me to wrap my head around the 2 / n^2 part.

charyeen94 Says:

May 3, 2012 - i dont understand why you would only use 2/n and 1/n and forget about the rest in the middle?

rgrafton Says:

May 7, 2012 - how is n^n always n in a series?

rgrafton Says:

May 7, 2012 - that's just because infinity isn't a number at all. It's just a concept used to understand that there is no largest number. 1^anything is 1 though... That's really the point of using limits if you're going to use infinity. go to wolframalpha and put this in: lim as n approaches infinity 1^n

FMAZON3 Says:

May 8, 2012 - lol add half and half to get a quarter.

dpetrosiann Says:

May 8, 2012 - couldnt we have used the direct comparison again for the second one and avoiding doing limits?

seddie777 Says:

May 9, 2012 - -_- Don't say he is wrong... When you multiply you add powers, you don't multiply them. so your problem would be 1/2+1/2 which does indeed equal 1, so it does equal n. To make it equal to n^(1/4) you would need a power to another power (that is when you multiply powers. So, [n^(1/2)]^(1/2) would equal n^(1/4)... Don't mess with JMT man

borqies Says:

May 13, 2012 - omg I love you man, in a brotherly way XD

izisvi Says:

May 15, 2012 - think about what you said... n^(1/2) is the square root of n. consider n=4. 4^(1/2) = 2. 2*2 = 4. not 4^(1/4).Multiplying numbers with exponents is a slightly different rule set than multiplying fractions.