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The link to the story in American Scientist is outdated; the current link is this.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 =100101/2 = 5050
2+4+6+ +100 = 2(1+2+…+50)=25051/2= 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