Hi. What if I wanted to find the sum of all even numbers between 80 to 560?

I like your ‘Many explanations will just give the explanation above and leave it at that. I won’t.’

Kudos on your dedication. I have bookmarked your page for future reference.

Best regards and good health,

Leonard Juska

Costa Mesa, CA USA

P.S. If there ever is time, I want to revisit a book I read as a child called

The Trachtenburg Speed System of Basic Mathematics by Ann Cutler and Rudolph McShane of the work by Jakow Trachtenburg. Bantam Books 553 07020 150 First printing 1960; I have a 1973 copy. Intuitive adventure.

@Jenn: Hi Jenn, you could try matching up the numbers like this (using technique #2):

80 82 84 86 …

560 558 556 554 …

and then dividing the sum by 2.

@Leonard: Thanks for the comment! Glad you enjoyed it; that looks like an interesting book

Thanks alot

Thank you so much for that explanation. I had learned this same formula in my Maths class without knowing how it had been derived. I had to use this formula to find the sum of series in arithmetic progression, and now, I wonder why I hadn’t seen this site before.

Keep up the good work!!

Hey! Thanks a lot! You saved my exam!

…and me too!

Elegant and satisfying!

The link to the story in American Scientist is outdated; the current link is this.

For adding the odds (whether the no of numbers is odd or even ) this also works well. Using the same anology given by you,

1+3+5+…n= (n+1)^(2)/4

For e.g.

1+2+3+…+100 =100*101/2 = 5050
2+4+6+ +100 = 2*(1+2+…+50)=2

*50*51/2= 2550

1+3+5+…+99 = (99+1)^(2)/4=100*100/4 = 2500

i have a question any one can help me

adding n numbers formula x = n(n+1)/2

please give the formula to identify value of n if x is given

for n= ???

Please it urgent

[…] Intro: Mental math shortcuts, adding 1-100, how to learn math, understanding averages […]

I love mathematics so much! Thanks for explaining this so perfectly!

amazing site, thanks for all. You give an enormous inreachment for math. Magdi

thank you, that helped quite a bit!

thank you soooo much!!! u helped me a lot!!!

@Magdi, Maria, Mae: Glad it helped!

[…] Jason Sadler has been selling the upper part of his wardrobe ever day of 2009 to companies that want him to wear a t-shirt with the logo on it. His pricing structure is very interesting though. He’s sold January 1st for $1 and is selling December 31st for $365. Every day in between goes for the price of it’s day of the year. I wasn’t to excited about that until I calculated (using Gauss’s method) how much money he’d be earning for the year: $66,795! […]

[…] Jason Sadler has been selling the upper part of his wardrobe ever day of 2009 to companies that want him to wear a t-shirt with the logo on it. His pricing structure is very interesting though. He’s sold January 1st for $1 and is selling December 31st for $365. Every day in between goes for the price of it’s day of the year. I wasn’t to excited about that until I calculated (using Gauss’s method) how much money he’d be earning for the year: $66,795! […]

i have a Q :if i wants to add from any other no. to 100 ??

thx alot