Alternating Series Estimation Theorem

[NKGENERATION]

Making life easier for calc students everywhere

[kwazimoto44]

thank you!!!!!!!!!!!!!

[midnightstars0]

Thank you so much. This went right over my head in class lol.

[chocochris93]

your videos are now an essential part of my studying. Thank you very much!

[ceciliasmile]

Thank you Patrick! It is very helpful!!!

[klayworldsniper]

I have a test in an hour and didn't understand this stuff. Now I do. Thanks so much, you're my pre-test ritual.

[geebauer]

Youre a boss Pat

[patrickJMT]

@geebauer just doin' what i can

[chulminh]

Hi Patrick. If I want to solve it algebraically, and within 0.001, do I set a of n equal to 0.001? Thanks

[koreahiho]

Hi Patrick. If you don't mind could you help me please?

So I have to find 3 diffrent values of u

( (-1) ^n * (1/(1-u))* 4n ) / (2n)! = -1/2

I tried to do with estimation...but I have no idea...

then I tried to do limit comparaison, but it does not tell me the sum of the series.

or should I use Taylor theoreme?

Please I am literally begging you how to solve this.

Thank you

[jasonjkeller79]

Is it correct to assume that this will work for an alternating power series as well, given a situation where we know what n and x equal?

[3MOloviie]

but how do we know which one will give the answer to four decimal places if were not allowed a calculator? xD

[GammahooX]

Your result is not correct within 4 decimals - with an error of 0.000023 the actual result could be 0.098785 + 0.000023 which is 0.098808.

If you just take the first 4 decimals and compare them: 0987 =/= 0988.

[YouGotSchenkd]

But Patrick, if this method only works for alternating series then what do do for everything else?

[theotheroleander]

THANK YOU SOOOOOOO MUCH THIS WAS SO HELPFUL!!!! i finally understand this thank you!!!!!

[ronniemonnie]

Wait... how do you know which term is the first neglected term?

[ronniemonnie]

@ronniemonnie nevermind

I really need to learn to just watch the videos all the way through

[xrockerchick4lifex]

This was soooo helpful! I was stuck on a problem like this for a half hour and you saved me in 30 seconds!!

[skunkyconkey]

Thank you patrick! I missed some lecture and couldn't make it to the calc tables (tutors) cause i was sick. Trying to decipher my book can be a head ache. Wow, i think my hair stopped falling out.

[falastinicoor]

iloveyouiloveyouiloveyou

[akmcferran]

I've used your videos to replace my AP Calc teacher :) I think I have a chance of passing the AP Calculus BC test now :O

[NMShredder1080]

I just found your videos, Great work man!

I'm studying for my calc 2 test tomorrow and the only thing I didn't understand was this estimation theorem. (missed that class)

Now I get it and I'm confident for my test. Thanks!

[hen555]

learned this in 10 minutes what wud actualy take 1 hour if i tried learning from the book.

thanks!

[blkfsty555]

I LOVE YOU PATRICK!!!

[crazycanadian132]

THANK YOU SO MUCH. I was so lost before this

I had to find the number of terms for an alternating series of (-1)^(n-1)*(1/n^3) to get an error of 0.01 and I just for the life of me couldn't figure out how to approximate the minimum numer of terms before i watched this!

[iammaxhailme]

Error is at most size of first neglected term

That makes a lot of sense. Why bother with the whole rn > s-sn? I should tell my prof to just say that. <__<

[patrickJMT]

@iammaxhailme well, this only works for alternating estimation theorem

[iammaxhailme]

@patrickJMT

I was expecting either an alternate estimate or an integral estimate to show up on my exam (that I took between my last comment and this one) but it didn't anyway

[ammarshaikh1000]

thank you

[ammarshaikh1000]

thank you

[lilitrichie]

this 10 minute video was more helpful than my professor explaining for 2 hours.

[23youwatch]

u are the BEST!!!!!!!!!!!!!!!!!!!!!!!!!!­!!!!!!!

[fhunkymonkey]

so for both taylor inequality theorem and this theorem, the size of the error is the next term? ex. summation of n=1 to n=4 term of a function will have an error less than or equal to n=5.

[patrickJMT]

@fhunkymonkey no, taylor's theorem does not work that way; it is a bit more complicated

[FaiththeHairstylist]

Awesome. I missed class Thursday, so now I'm getting caught up. This theorem is actually really cool when you think about it.

[patrickJMT]

@FaiththeHairstylist yep, and it makes total sense!

[ShivMan007]

the pinnacle of social media importance is right here. u sir, are awesome.

[patrickJMT]

@ShivMan007 ha, thanks : )

[varung92]

U are a milllion  times more helpful than my Calc Prof!! Thanks! :)

[ea33ie]

Thanx it was helpfull..

[fizzmaverick]

omg so simple...thats not how it was in my text!

[alrasw]

love u!

[saqajaan1]

Hi Patrick, Thank U for your math video help. If I have a series starting with one to infinity of (-1)^n(n^n/n!), how dow I show that the series either diverges or converges using Alternating Series Test, generally I have problem with series involving factorials. Thank.

[siriusblack9999]

actually i noticed something with the second example here, apologies if this was already mentioned or if it's an invalid argument

but the 6th term would add 0.000023... to 0.098785...

that makes the new number 0.098808, with the next number substracting some part(probably smaller than 0.00001), so the 4th decimal is actually incorrect

[3Daybreaker]

Thank you so much for your videos. Great for quick review!

[NicholasAABBoy]

I just noticed that there should be a minus sign after the 6th term :)...but anyways your video is awesome

[cacaloveforever]

hehe ;)

[cacaloveforever]

lol writing in wet erase markers ;)

[patrickJMT]

@cacaloveforever i have gone back to the sharpie and paper

[ecaep86]

@patrickJMT help!!!!!!! find the sum of the serier : sum from n=0, to infinity of (-1)^n 5/4^n and also another question i dont get: use the concept of a convergent geometric series to write the number 2.7181818.... as a ratio of two integers.....I dont get these two question and obviously my tutors at school dont get it either.....PLEASE Help i love your videos

[pshhockeyplaya]

Thank you thank you thank you! I had mono and missed all these lectures, and the book wasn't really helping me but you made it really easy.

[MrJsnL211]

thanks so much...your videos are really helpful!!

[jieun7543]

(at 5:00) hey can some one explain to me how to take the limit of n/8^n as n goes to inifinity? not that i dont trust him... i suddenly blanked out... can somebody explain to me please? thank you

[astrobiologist]

Thanks for the good review. We have an exam tomorrow in Calc 2 on infinite series. I've been trying to find information on how to determine whether the error for an alternating series estimation is an overestimate or an underestimate...

[al7rbi1981]

what I say?:)

You are awesome

[kevinkk26]

still dont get it i must be slow

[dirtybitbucket]

@kevinkk26 What part don't u get? Do u

understand what the theorem means? Do

u know what alternating means? Do u not

see y it is true? The video doesn't cover the

proof of the theorem.

[buttman20]

Thank you, your instructions are clear and coherent! It makes perfect sense, and I definitely understood this at an applicable level!

Be my teacher!

[jlahey1]

arse of n. awesome.

[cutcub]

Thank you

[theone2088]

In the first example, he added a +1 to the ^n, making his signs right. (at 2:05)

[dirtybitbucket]

Thx. I didn't see the +1.

[Nanumir]

I recently had a friend of mine ask me to tutor them in Calc II, I was ok on most of the convergence/divergence problems, but I did not know where to go with this, I wish I ran across this sooner.

noyce job mate

[readnoar]

you are sooo helpful my teacher didn't go over this in class and then put it on the test

[sohaib785]

lol

[SevereTstormFan]

Looks like you have trouble writing you're sigma E. It is annoying to write. I am learning alternating series now by the way. Its certainly easier than most Calc topics.

[roni51154]

I almost received a perfect score on my last differential equations test. My one mistake was using 'bn' instead of 'bn+1' when estimating the error on an alternating series. *face-palm*

[patrickJMT]

near perfect sounds quite alright to me : )

[fiorellavt1]

thanks! it is clear now

[patrickJMT]

hey! a 'B' is good! nice job! : )

[harrypatel910]

hey Mr.patrick ....i watched all your videos for my calc-2 class last semester ....it really saved me from failing and i finally eneded up with B instead of F...!!! thanks a lot man...salute u ...and flowers...

[roflcopter76]

This would be awesome for me, unfortunately we arent allowed a calculator in my calc class.

[Calculusman08]

Nah, you're good man. You said convergent, I'm sorry. I just look for exact stuff. But great video man. You made it really easy to understand. Keep it up!

[patrickJMT]

ahhh ok, it is conditionally convergent : )

in many books, when one first learns about alternating series, you do not yet know about absolute/conditional convergence, so i figure it would just confuse people to throw that terminology in there at that point

[Calculusman08]

Oh yeah man no worries. You've got some great stuff here on youtube. Keep up the amazing work! We need people to spread the word of math. You do it very well.

[patrickJMT]

thanks and thanks!

you going to study math in college?

[Calculusman08]

Am, lol. I'm a math major now. I'm in Calculus 2 now. I'm taking Calc 3 and Probability next semester. What's your story?

[patrickJMT]

my story is short and boring

[Calculusman08]

Oh, nothing big, but the alternating harmonic series is actually conditionally convergent. I just wanted to say that. thanks.

[patrickJMT]

did i say something different - i do not want to watch it all and find it out

[santaslick]

Extremely helpful, thank you so much. I have a midterm on this tomorrow and you just explained this better in 10 minutes than what my professor could do in an hour long office hour session.

You are a god of math, good sir. Keep it up!

[patrickJMT]

ha! god of math! not quite, but i appreciate the nice words all the same! good luck on your midterm!!

[brco2003]

were you doing those 8-powers in your head or calculator?

[hyp3o]

Thanks so much for posting. Very clear

[love2CUsmile86]

Thank you so much! I'm currently taking Calculus. My teacher is nice but her teaching style is not simple as yours. She teaches to get the lesson done so she can get her paycheck, not because she wants use to truly learn math. I visited your website and it helps A LOT. You made it so much easier. Thank you.

[steveofreeblind]

you are amazing

[patrickJMT]

ha! thanks : )