Deriving Formula for Sum of a Geometric Progression

[@ricardovergara6430]

The man is an excellent teacher, the change in his voice's pitch is alone to keep the class awake and engaged. You're a rare breed Professor.

[@tensaijuusan4653]

I am 64 years old and I wish you had been by mathematics teacher. A good explanation and understanding of how a formula is derived rather than just a dry presentation of its mechanism can really turn on a light bulb for so many students.

[@buzz_is_here]

Dude, I'm a software developer, went through (admittedly only) one year of CS UNI and this is still the best lesson on GS I've seen yet. Thank you!

[@esthero114]

What is really amazing about Eddie's classes is that he gives his students the chance to experiment with different ways of trying to solve the problem instead of just giving them the answer. That way they understand why the wrong method didn't work and why the right one did.

[@eshabaweja]

Watched this back in 2017 for school, watching it again in college while solving recursion trees :)

[@craighennessy3183]

I wish I had teachers at school with a tenth of your passion for teaching, i would have been a much better student. Brilliant stuff keep it up Eddie!

[@JulianGonzalez-ej2fi]

This lecture is important compared to most of the other ones because I came across this video about after 6 videos, that did not care to explain why we subtract Sn and rSn. Thank you for explaining that.

[@rach8360]

saving my maths a level grade one video at a time thank you!

[@qtkd1819]

ive been looking how to get that simple formula from SUM. Thank you so much!!

[@microhoarray]

Oh my goddd this is brilliant. They always forced us to memorized

[@arcadegamingpro8010]

Wow great explanation sir really from now you are only my new online Math teacher ☺☺😊 thanks alot watching from INDIA.

[@thehungryinvestor]

Absolutly lovely way of explaining, may you make more and more videos explaining things so easily and in a fun way. These kind of teachers actually add value in the life of students, thanks for being a teacher like you are :) :).

[@crisgwyngieponferrada2039]

I'm a teacher. And I get ideas from you. Thank you.

[@Someone-zx7xd]

I really feel like I am stupid. Why was I not able to figure out this simple proof even after thinking for many days?

[@ProofDetectives]

Thank you for your explanation. Have a good day.

[@avanthikakatari960]

thank you for your explanation

[@thebadagnostic]

Amazing explanation!

[@commenter4799]

I waited 14 years to go to college, and these videos really help me. I have a book, but it couldn't be a bigger piece of crap even if the pages were made of crap and those were printed on with ink made of crap. Even if they used glue made of crap to bind the book, covered it in packaging made of crap, and put it in a box made of cardboard, it still couldn't be a bigger piece of crap. With how many steps they skip in the examples and explanations, a professor would dock points if he were grading it, yet we're supposed to follow along trying to learn new concepts. In summary, I am quite dissatisfied with my calculus textbook.

[@noodletropic]

Your statement rings true while humorous. Hope it get better for you.

[@innochilondola8422]

Well articulated

[@Pravinsahu-qf9bb]

No words. Only emotion😢

[@Bill-xn9tp]

Beautiful.

[@hhtan1346]

What is the meaning "the whole things will collapse when multiply by r?" And why minus r(Sn) by Sn will get the sum of it? It's seem like counter intuitive because how the first person that create this formula will know that multiply by r and subtract them will get the answer?

[@divyoroy9056]

As he said, as multiplication occurs in a geometric profession, we need to cancel it with multiplication. Just like we did it for arithmetic progressions, except it is addition. Then we subtract them to cancel the terms except for a and ar^n.

[@sashalo1194]

HH Tan I too was wondering how the “first person to solve this” would have come to the answer. What is important to realize is that the formula for the sum is already given to you, as a plus ar plus ar^2 ... but as you can see it is long and cumbersome making it difficult to solve for efficiently. Therefore it makes sense to try to “cancel out” as many terms as possible while still being able to solve for Sn. What this derivation does is pairs all of the middle terms in two equations to cancel while still being left with Sn(1-r) on the left, allowing to solve for the sum without having tons of terms to add, creating a generalized form that only depends on the three things that define the series: first term, common ratio, and number of terms.

[@divyoroy9056]

@@sashalo1194 yep you're right

[@morpheus6104]

@@sashalo1194 Yeah, I saw it as r effectively shrinking the Series Sn from the first and last term.

[@ljdowle5431]

SO GOOD!!!

[@jaym6552]

Sir, I thought we add terms when doing the process of elimination. Why are both positive terms in the sequence, ar and etc., canceling each other out? I am still slightly confused on this. I sincerely give my thanks for these videos. We are just given formulas to memorize and often not taught why and how they work. I understand that when my school days are over I may not remember the formulas. These videos truly help with that.

[@parthrajagopalan5302]

They cancel each other out as we are subtracting the second sequence FROM the first sequence (or vice versa). When we do that each corresponding term that is equal will cancel out and we'll be left with only 'a' and 'ar^n.

[@dsp6742]

Exactly. The Indian Education System is focused on what and not why or how.

[@hellryderplayz1854]

@@parthrajagopalan5302 yeah, but WHY do we do that, how does the Sn-Sn(r) function help us find the sum of the series?

[@danyaaaa31]

@@hellryderplayz1854 I guess we simply tried and realized that after elimination of terms we get a formula for Sn.

[@hndjijwhvuwohhhrmnd]

amazing, thank you

[@uniquemathematicsclassesdo2761]

Please define one example where use GP concept in my daily life , I have an interest about this topic Thanks

[@SamyakAditya]

Thx for amazing explanation

[@maxwellsequation4887]

Me who tried deriving it with summation function and did in an hour, seeing him do it in some minutes : 😧😧

[@maxwellsequation4887]

@@amaldev3462 yes it's way more dumb Simple summing up and trying to derive stuff

[@pianoforte17xx48]

Well he planned for it. Proving is not on glance

[@TechnoSan09]

But u tried and even finished😉

[@zizo-ve8ib]

I love your videos so much for real I'm a fan I have a question though, what happens if I do it using calculus, because I tried it and got the sum = a(r^n -1)/ln(r)

[@ruxuesim3043]

Thank you so much!

[@mrhoho]

thanks for sharing

[@bidhancreationsudeshaschoo9924]

The sum of the 5 terms of a geometric series is 93 and the sum of the first 8 terms is 765.Then answer the following questions.Find the common ratio and first term.plz solve it.

[@adleytahsin1083]

Helped a lot

[@fazepug1982]

why was the last term (n-1) and not (n)? wouldn't (n-1) be the second last term?

[@alphonseraynaud976]

there's a literally a student who asks the same question and he spends almost a minute answering it

[@JannahMa]

Finally i understand this

[@Obase-Aboli]

A capital increase in value four times one in t years, if the rate of interest is given to be 8% p.a. Determine the value of t

[@jashwamesfin1392]

what grade do you teach

[@chetnapandey193]

awesome

[@khaldoonmohammed6025]

شكرا جزيلا thank you

[@samb9645]

Hell yes!! I get it!!!

[@ShehabElshehabi]

How can I proof an = an r^n-1 🧐

[@You-bb5wo]

an=a1r^n-1 if you mean that then watch this video kzbin.info/www/bejne/kGfNqYuimdqHiLc

[@djmelo6247]

what if r=1?

[@danyaaaa31]

This formula was derived for r not equal to 1, as we divided by (r-1) when solving for Sn. But we can see that any "geometric progression" as r = 1 is in form a, a, a, a,..., a,.... So the sum of first n terms is just a*n. But we actually don't usually call this type of progression a geometric ptogression.

[@djmelo6247]

@@danyaaaa31 thanks for the anwser, understood

[@danyaaaa31]

@@djmelo6247 edited my answer

[@asiansocrates]

Singaporeans are smart

[@RamKumar-sw3yn]

I have seen that one. Do u have another one?

[@25kirtan]

♥️

[@daydreamer05]

Your channel should be subscribed by me.

[@jacobhouston1655]

This wasn’t helpful. I didn’t understand why r is raised to the negative power at the end of the series. Not a good introduction.

[@pianoforte17xx48]

Lol he just explained it to a student.. the -1 indicates that the number of terms should be n, and the 1st term is simply r⁰ so the n-th term should be rⁿ-¹ because you count the terms as "1,2,3,...,n" not as "0,1,2,...,n" because there's no such thing as 0-th term

[@alphonseraynaud976]

this must be one if the worst comments I ever read. He explains it perfectly well, answering every students' questions (including the one you ask). Please just listen to the video instead of writing such a negative comment which not only makes the video look bad although it definitely isn't but also just makes you seem dumb. Thanks