This is the first time I have seen a visual representation of the comparison test and it really sticks with me. It appeals to my tendency to look at things intuitively. Thanks!
I just want to personally thank you for helping me pass Calc. You have truly helped me earn my bachelor's. You are so cute and so smart, you make learning fun, regardless of the amount of "right"s that you say. Anyway, thank you.
I'm an older student returning to school and am so thankful to have an internet full of resources like this! Thank you for taking the time and providing this free of charge. Many thanks, Krista!
You're welcome, I'm happy to help! I've worked with so many people who go back to school after being away for a lot of years... LOVE that you're jumping back in! :D
This seriously helped me so much I can't thank you enough. You really know what you're talking about and know how to teach it. I wish you were my TA haha
I don't know whether you believe in heaven but you will probably go to heaven for helping so much people with your videos... By the way your voice is very beautiful( you should try singing sometime). It's a pleasure to listen lessons. Some professors have voices that tortures ears they should hear you and be ashamed. Thanks for all these videos. May the math be with you:) ;)
ur voice is so cute - i die everytime u say Hi everyone and BYE lmao but on the serious note this was an excellent lecture and it helped me a lot (especially the graph!) thank you soo much!
your definition at the top of screen is wrong. b_n doesn't always need to be greater than or equal to a_n. In fact ,just like you say, b_n must be less than or equal to and divergent to conclude a_n as divergent. I think you meant to say that they both have to be series with positive terms.
I understand the an and bn, but what exactly are we trying to show. I see how they behave similarly when they might only differ by a constant, but am a little confused. Are we just showing that one of the series might be offset but still retain its shape? Is this similar to changing the y intercept on a graph, and showing that the line just shifted?
calc 2 has been such a nightmare, thank you for all of your work to help me and other people through it.
sirspamsalot2 I'm glad I could help!
This is the first time I have seen a visual representation of the comparison test and it really sticks with me. It appeals to my tendency to look at things intuitively. Thanks!
I just want to personally thank you for helping me pass Calc. You have truly helped me earn my bachelor's. You are so cute and so smart, you make learning fun, regardless of the amount of "right"s that you say.
Anyway, thank you.
I'm an older student returning to school and am so thankful to have an internet full of resources like this! Thank you for taking the time and providing this free of charge. Many thanks, Krista!
You're welcome, I'm happy to help! I've worked with so many people who go back to school after being away for a lot of years... LOVE that you're jumping back in! :D
I need your help to spread the word! ;) Thanks for the comment, glad I could help.
This seriously helped me so much I can't thank you enough. You really know what you're talking about and know how to teach it. I wish you were my TA haha
I'm so glad I can help! :)
You are an absolute blessing. I have been watching you since Cal1. I always search for your videos first. Thx so much.
I'm so honored, thank you!
Bless your heart honestly! Thank you so much for helping us fellow students understand Calculus!!
You are so welcome, I'm happy to help! :)
I use an image, and then write on top with a drawing app (sketchbook in my case, or something like photoshop). And then screen record the screen. :)
Seriously your videos are such a blessing. I finally understand calculus. Thank you!!!
That makes me so happy! Thanks for making me smile. :)
Thank you so much for explaining the concept and giving the example. The concept explanation helped me not memorize a definition :)
I just took my sequence and series exam and got an 87!! Thank You for making such great videos and explaining everything step by step.
That's so awesome! Thanks for letting me know. :)
I don't know whether you believe in heaven but you will probably go to heaven for helping so much people with your videos... By the way your voice is very beautiful( you should try singing sometime). It's a pleasure to listen lessons. Some professors have voices that tortures ears they should hear you and be ashamed. Thanks for all these videos. May the math be with you:) ;)
Glad I can help!
awesome the graphs really made learning the rules easy thank you
awesome! i'm so glad! :D
Great stuff! Easy to follow, easy to understand!
Thanks!
ur voice is so cute - i die everytime u say Hi everyone and BYE lmao
but on the serious note this was an excellent lecture and it helped me a lot (especially the graph!) thank you soo much!
You're welcome!
It says at the top that 0
You rock giiiirl! Thank you for all your time. Namaste
+Allisin L Thank you so much!
Awesome! Glad you liked it! :)
wonderfully explained!
+Akshay Sharma Thank you!
Awesome! That makes me so happy!! :)
Hey! I was wondering if it was still right if there was (square root of n) - (a number) on the numerator?
your definition at the top of screen is wrong. b_n doesn't always need to be greater than or equal to a_n. In fact ,just like you say, b_n must be less than or equal to and divergent to conclude a_n as divergent. I think you meant to say that they both have to be series with positive terms.
Very helpful
i love you too!! :D
Love you
I understand the an and bn, but what exactly are we trying to show. I see how they behave similarly when they might only differ by a constant, but am a little confused. Are we just showing that one of the series might be offset but still retain its shape? Is this similar to changing the y intercept on a graph, and showing that the line just shifted?
you are really amazing ,
Yikes! Awesum teaching.....Your videos were really helpful
(1) You're beautiful (2) Great calculus help. THX!
I'm really happy you like them. :)
Best video on the comparison that I have seen thaaaaaaaaaaaaaaaaanks
awesome! i'm so glad!! :D
Thanks for the video, but please don't say 'right' so much times!
Sorry about that! I'm working on my 'ums' and my 'rights'. :)
Thank you!
You explained it very easily through the graphical method.
Thanks! Glad you liked it.
marry me?
your explanation of the relationship between bn and an is fantastic, this helped soooo much thank you
+Luben Roftus-Cheek You're welcome, I'm so glad I could help!!
thanks
This was really wild, .."beautiful", made me think. Thanks
You're welcome, I'm glad you liked it!