Showing a Series Diverges using Partial Sums

[oldschoolguys]

Hello Patrick. You are one of the best teachers who explains everything very clearly. I used to memorize(cram) in college, but now understand the theorems perfectly. You have a passion for teaching and am happy to have a blessed & talented mathematician like you. In my country, this section was actually called Real analysis. 2/3 of the class failed the exam, but I passed only with a B. (1995) I was a statistics major. I will definitely donate in your website. Thank you again. Keep up the Good work. Please make more statistics videos of (multivariate analysis, stochastic processes, estimation theory, hypothesis testing, sample survey designs, ANOVA/ANCOVA, Time series analysis, Operations research). I also did advanced Physics, Chemistry, and Engineering.

[funnello]

50% final on this in 9 and a half hours! These videos are lifesavers :) Thanks for all the help :)

[jkbdfrd]

all of your videos help so much you really are helping a ton of people with all this work you do

[sleeplessbird]

Very neat, we spent half an hour doing all other tests and didn't think about writing out some terms. Thanks for the vid

[joshuastier]

So, SO SO SO SO much better than khan academy. You are my savior dude.

[RAJENDRAKUMARVM]

i am in 1st semester...i actually mugged my maths till school...now in coll...i cant dare to continue...so bunked all math classes..now i hav my 1st sem assessment in math within 2 days.Afraid of a fail... just browsed web...led to this wonderful tutorial...Thank u sir...really thanks..

[fredxx]

when I read my calculus book, it looks like a bunch a formulas, but after spending 30' watching your videos, everything becomes clearer :p, thanks patrick.

[AndLi]

you're the reason why i got 100 on my last calc Thanks to you I understood graphing polar coordinates.TY

[Ravel]

PatrickJMT = giving me A's in math since 2008. Why are you so cool?!

[BriantehBoss]

I have been watching your videos for the past 3 years, you are amazing!

[longhornsfan]

I rarely sign in to youtube but I did just so I could comment on this video. Awesome stuff! I wish I would have found these videos earlier. HUGE help! Thank you!!

[patrickjmt]

yes, i actually do not think i have a video for the remainder theorem estimate - one of the few things missing from my 'series' series

[PrivacyKingdoms]

at around 4:40 (before and after)... when patrick started canceling out the ln's he ended up with a -ln(1) being the only one not crossed out (he physically crossed it out but there was no +ln(1) to be added to it.) -ln(1) is zero. There was also a ln(6) but that would have been crossed out if the series kept on going forever and every other following ln(of a number) would have been crossed out (ln 7 ln 8 ln 9 etc.). So why isn't the summation = to -ln(1)... or zero?

[ektrules]

Wow, what a coincidence. That's the exact same problem I was having trouble with on my homework. I actually solved it with the Integral Test though. Had to spend a lot of time looking over a lot integration tables and logarithm rules. This is much easier, thanks.

[desena]

Wow, I can't believe I'm actually understanding. Thank you so much!!!

[goosebump]

Thanks dude, this really helps me understand it better.

[Loveboat]

i watched this in 1080p! awesome job on all your vids, u saved my life!!!

[Suejchang]

this dude helped me get an a in both semesters for calc ab and i passed with a five

[iceskater]

Also, thank you for posting this video!
I did this by taking the integral. I got the same answer but your way is definitely easier :)

[EagleLogic]

Hey Patrick... I know you're one busy ass dude, but I am running out of problems to do in this 1, 001 problems book you wrote! Maybe one day you could write another book and include more cal 2 topics like series and vectors! Thanks for all you do!