How to Sum a Series! EPIC Math

Update: I am not available for tutoring! But still alive, :) Meanwhile, so many students have personally recommended Target Test Prep for GRE / GMAT that I asked them for a unique discount code, TestedTutor10, for this link: targettestprep... It is so useful to know how to sum a consecutive series of numbers, be they integers or multiples, evens or odds. Even with a calculator, could you quickly sum the numbers 1 to 50? I will show you the ultimate method for doing so, starting with beginner questions all the way to expert ones.
This video will also touch on sequences, finding the last term of a series and how to find the middle number of a consecutive set of integers.
I offer private GRE / GMAT tutoring online at a fixed rate of $140/hr. Please get in touch via the email below, or through my tutoring website: www.gretutorlo...
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The GRE and GMAT are two of most used graduate exams for those seeking to study a Masters Degree or Masters in Business Administration (MBA) degree. The Graduate Record Exam and Graduate Management Admissions Test have been taken for over 50 years and are taken by approximately 600,000 and 300,000 people worldwide annually, respectively. These exams are typically taken between the ages of 18-40, by those who have completed, or are about to complete, their Bachelors Degree.
Grateful for any support: / testedtutor If you’re now ready to get into your dream MBA program, my former student, Angel, is offering virtual private Admissions coaching. She was admitted into Harvard Business School, The Wharton School of Business, and Columbia Business School (accepted into every school she interviewed for) after graduating from UCLA with a degree in Communication. She also got 3 perfect scores on the GRE’s Analytical Writing Assessment (99th percentile).
Here is her link - linktr.ee/ange... - and you can reach her at [e-mail] with the subject line, “PHILIP SENT ME.”

[@srishtimittra3656]

After watching your videos i always feel compelled to express my gratitude for the amazing work you are doing. Thank You so much Philip :)

[@TheTestedTutor]

Thank you so much Srishti!

[@joeboxter3635]

@@TheTestedTutor Indeed. By the way, Euler likely did come up with the method. But Gauss did it at age 7. Credit must go to the first, and that would me Euler -- my favorite. Still you have to admire Gauss.

[@LordofG]

You are the reason I will pass my GRE tomorrow. I have to say you are so good at teaching. You're slow enough for me to follow and you explain everything in great detail. I've seen so many of your videos here and saved so much money by doing this instead of classes. I'll post tomorrow after I'm done just to show you how much you helped me. KEEP IT UP!

[@TheTestedTutor]

Good luck Esfet. Thanks for the motivating words.

[@cardiyansane1414]

how did it go? i hope you come back with some good news and motivation for the rest of us

[@LordofG]

@@cardiyansane1414 I had to change the date. Family emergency unfortunately. No one died or anything like that but I'll be doing it on July 7th now. This is a good thing though because it gives me more time to watch @TheTestedTutor. 👌

[@RandomGameCaps]

@@LordofG Any update? How'd it go? Eagerly waiting for your reply.

[@dan-gu1ty]

@@LordofG how'd it goo?

[@nipunsrivastava7469]

You explain everything so so beautifully. I have been looking at various videos by a lot of other teachers too and while they are all great, they don't quite bring home the understandings like you do. Thankyou for these videos.

[@natarajanparameswaran6752]

We can also find the no.of terms by AP formula an= a1 +(n-1)d

[@simsimmons8884]

Even a simpler way to approach is "for even numbers, the sum is 1/2*n (n+1)." So for odd numbers, solve for one less than the total and add the final odd number.

[@anahitadeo9670]

I just want to say thank you, you literally helped me figure this out in such a short time. I have been trying to understand the concept since quite a few months!

[@tommyshelby2020]

One of the most helpful videos on the topic on the internet! Thanks philip!

[@anushaashivshankerdas5799]

I was craving for a more structured, step-by-step approach to attempting quant. Thank god I found your channel. Hope I'll get a better score on my retake.

[@ChengaPonga]

Great work as always! I usually find to easy to sum using (n/2) (1st term + last term). This is built on the fact that the sum of first and last term is always constant when moving inwards on a list starting from endpoints. We divide by two because the sums are counted twice.

[@TerranIV]

Thanks for this great lesson! I am glad I stuck around for the last question because I didn't get it until that final problem! :) This is a great formula to remember for everyday life!

[@TheTestedTutor]

So glad to hear Terran

[@peterbankole6055]

Thank you "The tested tutor". You are awesome. God bless you.

[@MeganMunro-e4y]

Your videos are so helpful!! I've been using other resources for 2 months and I feel I've retained more from your videos in just one week. Thank you so much!

[@isaacabanyi2131]

Thank you, Philip. Great delivery

[@tanishakapoor7413]

Hi Philip, I have never been so intrigued and hooked to quants. It's all because of you! Keep up the good work :)

[@salonidoshi8269]

You're terrific, Philip! Thank you!

[@ritikashaw440]

Love your channel! You are a great teacher! Thank you for existing

[@Dannydefeato25]

Have you taken the GRE yet?

[@ritikashaw440]

@ I am about to give my GMAT

[@reddaxtor5662]

Thanks a lot! I've greatly benefitted from your video series. Really grateful!

[@mpho_madiba]

Thanks a million Philip!! ❤

[@stevenrix4515]

You're amazing Philip! Thank you!

[@shritisingh1301]

Philip when do we use that other formula for sum : N(N+1)/2 ? where N denotes the number of terms

[@vishwagandhi8805]

Gonna binge watch your videos tomorrow!😁

[@TheTestedTutor]

Enjoy!

[@sumaiyaaralima3563]

Glad to see your quant videos.Plz make more quant videos that will be helpful for us.Stay Happy,stay blessed..

[@TheTestedTutor]

Stay blessed Sumaiyaara! :)

[@xxmuneyxx]

As always, amazing stuff! Thank you for all the invaluable tips :)

[@TheTestedTutor]

Thanks Derek

[@kay10481]

Thanks a tonnnn ! Most awaited video 🙏🏼👌🏻 Can you make a full video like exponents on probability , it would be a great help

[@TheTestedTutor]

Thanks kay, great idea

[@Manaswini2706]

This was a confusing topic for me. Thankyou for making it simple to understand 😊

[@elhamwalid8866]

A life saving method ❤

[@megank707]

Loved it 👍🏻👍🏻👍🏻

[@TheDallasDwayne]

Very interesting on the first problem. I thought Euler’s method was to add the first and last terms and multiply by half the number of terms. In this case, that would be 51 * 25 = 1275.

[@vishwagandhi8805]

Thank you tons!💙

[@mashawinchell1554]

Important to note that this method only works when each term is equidistant from each other. That is, the increments between each term are the same. I was confused as to why this method didn't work, when say the series we were summing looked like a(n) = 1 / (2^n). But it doesn't work because the middle term is not "the average of the first and last term." In this case, the middle term is much closer to a(1), than a(10), if that's the series we were summing.

[@anudeepsanpala5357]

Do vedios on circles shaded regions and also explain about minor and major

[@jairajsingh1850]

no

[@KyleMcCartt-nl3dl]

As always, thanks!

[@gilifromphilly8533]

Wow!! Thanks so much quick clarification - when you say "middle term", that's median right?

[@vishnagendra8959]

I have another formula for the advanced question where it is not necessary to know the last term N/2 [ 2 (first term) + (N-1) D ] Here, N is the number of terms found in the same way you taught. D is the increment In this case, D= 1 , N= 120 , first number is -54 Please do let me know if it is correct! Hope it helps

[@nishakapoor6979]

Hi Philip, Thanks for the video. Although, wouldn't it be much simpler if we go with the AP formulas?

[@TheTestedTutor]

Different students find different techniques easier for sure

[@brighttawiah3079]

But please hope we can use Arithmetic Progression formulae to find our number of terms . This can only be done when we know the last term. Finding the last term of a given series: L=a + (n-1)d where l=last term a=first term d=common difference n=number of terms

[@cardiyansane1414]

i was tempted to try that advanced only question ....

[@verdaarif]

Is the middle term the median and mean for the consecutive list?

[@shritisingh1301]

In case of sum of odd number say 10-100 : Increment will be 2 right?

[@TheTestedTutor]

Yep

[@parksunrpk1383]

Thank u Mr tutor

[@TheTestedTutor]

Np!

[@amanuelsidamo4152]

How can we calculate number of integers between 100 and 500, which are multiples of 11? Does the above formula for number of terms work in this case?

[@pokerformuppets]

A bit late, but it definitely does work here.

[@ashishsinha9035]

Thanks!

[@ankurupadhyay280]

How about using AP, GP and HP formulas?

[@TheTestedTutor]

That won't come up in the GRE/GMAT

[@ankurupadhyay280]

@@TheTestedTutor Thanks didn't knew that

[@p.j.882]

Can you use excel or Google sheets?

[@TheTestedTutor]

For sure. Not on the GRE tho

[@monkww]

Thank u soo much

[@ishanpathak2526]

Gold🎉

[@TunggulSagala]

Somehow I found arithmetic sequence formula is easier sn = n/2(2a + (n-1) * b)

[@brighttawiah3079]

From question 2: what is the sum of even numbers from 10-100? Solution: Alternatively, Middle number= (last term + first term)/2 =(100+10)/2 =110/2 =55 Find for the number of terms(n) Even numbers from 10-100 10,12,14,...,100. Using AP since the common difference are the same ie 12-10=14-12=2 a=first term =10 L=last term=100 L=a+(n-1)d 100=10+(n-1)2 100=10+2n-2 92=2n n=46 Middle term x number of terms 55 x 46 =2530 Hence the sum of even numbers from 10-100=2530.

[@mowmitaahmed]

Day 1(11/04/24) : Done

[@gg3675]

for the algorithm