Do you know what 1+2+3+4+5+6 through 365 equals?

INSIDE: There are so many fun and useful things you can do with compounding numbers, including saving some nice dough. Check it out!

So, here’s the question: Do you know what 1+2+3+4+5+6 all the way up to 365 equals?

I’ll tell you: 66,795. In case you were wondering ;)

Doesn’t that seem like WAY more than you would have guessed? Compounding numbers are cool.

I got on this kick yesterday of doing a fun year-long giveaway for you guys (“$1.00 a day which would increase by another one each day for an entire year!) but sadly realized it would bankrupt me. Sorry… Perhaps after I make my first billion?

And before you ask, yes – I started counting it all out until I realized there had to be a much better way. Like asking my wife :) Who then Googled it and found the algebraic equation for us to solve 1-2-3. (My boy Jesse from YNAB sent me this awesome Wiki How article afterwards which is even better – for those interested in figuring it out: Sum the Integers from 1 to N)

But while we’re not gonna do an awesome giveaway around this today, I figured we might as well apply this new found knowledge in a different way.

So here are a handful of other (smarter) uses for this compounding numbers formula:

  1. The 52 Weeks Savings Challenge. Instead of giving it away, SAVE $1.00 a week and then add another with each passing one until you end up with $1,378 at the end of the year! Kinda cool (and easy), as you might recall from earlier in the year when we happened to talk about this…
  2. Try saving a *penny* on top of each other every day. Which would net you a cool $667.95 if you can believe that. (Good idea, Chris Campbell)
  3. Use it to impress your friends who think you’re not that bright. (We all have those, believe me)
  4. And lastly, use it to prove to your parents that the internet contains more than just Facebook. I swear they think nothing good comes from the web sometimes…

I’m sure there’s a lot more you can do with compounding numbers (any math majors out there?), but unfortunately my coffee has just ran dry and I’m now thinking on fumes… So on that note I think I’ll go before I say something dumb. Have a formulaic day out there!

[Photo by WikiHow]

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  1. Jane Savers @ The Money Puzzle April 16, 2013 at 6:29 AM

    My number is 50%. I like my math easy. Live on 50%, 40% for debt and 10% for savings.

    You start putting brackets and numbers in an equation and I start running in the opposite direction.

    1. J. Money April 16, 2013 at 6:16 PM

      I like your math too! Hell of a strategy :)

  2. Tom April 16, 2013 at 7:06 AM

    I’m doing something wrong then. I keep getting 18300

    1. OriginalGriff August 4, 2018 at 10:42 AM

      It’s pretty easy if you think about it, and there isn’t a whole load of maths involved.
      Start simple: 1, 2, 3, 4, 5, 6 = 1 + 2 + 3 + 4 + 5 + 6
      Now rearrange them: (1+ 6) + (2 + 5) + (3 + 4)
      Which is obviously 7 + 7 + 7
      Which is also 3 * 7
      Since you always start with one, you will always get N / 2 “pairs” (the center “pair” will be just a single digit if it’s an odd number of terms): 6 / 2 = 3
      And you need to include the total of each pair: 6 + 1 = 7
      so N / 2 pairs, of N +1
      Which gives you N * (N + 1) / 2
      Or 6 * (6 + 1) / 2 = 6 * 7 / 2 = 42 / 2 = 21
      So for 356, it’s exactly the same process, just with bigger numbers: 365 * (365 + 1) / 2 = 365 * 366 / 2 = 133,590 / 2 = 66,795 pennies.
      (I used a calculator for this bit!)

      1. Cyrille February 11, 2021 at 11:56 AM

        Can this also apply to the dollar bill…I am trying to do something like that with 1$.

  3. Greg@ClubThrifty April 16, 2013 at 7:09 AM

    J, you’re making my head hurt. It is too early for all this math!!!

    1. J. Money April 16, 2013 at 6:16 PM

      (that’s what coffee is for)

  4. Mario April 16, 2013 at 7:23 AM

    While not quite growing this aggressively, my plan to pay down my student loan debt includes having the amount grow by a little bit every few months (for me, it’s $25 every few months) with the thinking being that as my salary improves, the farther I get away from grad school, and the more ways I’m able to find to be frugal, the more I’ll be able to pay

    1. Mario April 16, 2013 at 7:42 AM

      I should note that this is just one of a few strategies I employ to grow my payments a little (hopefully without noticing) and pay more frequently in hopes of banging this thing out more quickly

    2. J. Money April 16, 2013 at 6:15 PM

      I think stashing away *anything* consistently is good – so keep on going, my friend!

  5. Slackerjo April 16, 2013 at 7:40 AM

    I read (damn, I can’t remember where) about someone doing the 52 week challenge backwards, so week 1 = $52, week 2 = $51 etc. I thought this method brilliant as each week gets easier! By week 52 you could probably look for loose change around the house and easily find $1!

    1. Jonathan April 16, 2013 at 11:21 AM

      Unfortunately, the same principal that makes it easy toward the end also makes it nearly worthless toward the end. The idea is to build up slowly, like acquiring a tolerance for saving. Each week gets a little harder, but week 52 is not much harder than week 51 and you’re already used to saving $40-50 per week by that time anyway. If in reverse you can easily jump straight to saving $52 a week, why would you want to slack off that pace over time rather than building on momentum?

      1. Slackerjo April 16, 2013 at 4:59 PM

        Because my name is Slackerjo!

        1. J. Money April 16, 2013 at 6:20 PM

          haha…. I can see both sides actually. When I tried my 100 day pushup challenge based on the same method, I needed to start at around 10 cuz doing just 1 and then 2 and then 3 was just too boring/slow for me and eventually I gave up. Though in this case starting at 100 pushups a day would probably kill me!

      2. J Walton April 23, 2013 at 11:45 AM

        I played around with the numbers and saw I get the same result by putting away $53 with each pay period (24 total for me). I put it on automatic and watch it grow. I think either method is fine – just find out what works for you.

        1. J. Money April 24, 2013 at 9:27 AM

          Your way is a bit more easier w/ no fuss, haha.. I like it.

  6. Grayson @ Debt Roundup April 16, 2013 at 10:37 AM

    Ah, math! I am actually using the savings challenge for my son’s college savings account on top of what I already contribute. Nice work J Money! Thanks for making me think hard this morning.

  7. David April 16, 2013 at 11:19 AM

    My challenge has always been to save 100 dollars a week in a savings account that I cannot touch. The reason for this is it leaves me with $5,200 at the end of the year which is very close to putting away the $5,500 in a ROTH IRA for me for the next fiscal year. I have been doing this for a few years now and really like it!

    1. J. Money April 16, 2013 at 6:21 PM

      I like that too! Nice way to do it :)

      1. David April 18, 2013 at 12:11 PM

        Ya the trick is now I am getting serious with my GF and she is still in school. before I know it, Im gonna have to bump this up to 200!

        1. J. Money April 19, 2013 at 1:41 PM

          Will be worth every penny though :) We gotta do whatever it takes to keep our girls happy!

  8. MoneyStreetSmart April 16, 2013 at 11:24 AM

    Interesting way of looking at savings, I dig it! Kudos!

  9. Edward Antrobus April 16, 2013 at 12:25 PM

    It’s also really easy to figure out with a calculator. The function is called a factorial and is signified by an exclamation point. Just enter the last number of the series and then the factorial button on your calculator and it will add up all the numbers from one to the number you entered.

    1. Celina April 16, 2013 at 3:25 PM

      Factorial is for multiplying consecutive numbers, not adding them.

      1. J. Money April 16, 2013 at 6:22 PM

        MATH WAR!!

  10. Nick @ April 16, 2013 at 2:33 PM

    It is amazing how fast that adds up! Maybe compound interest isn’t the most powerful force in the universe…..

  11. Jake Erickson April 16, 2013 at 4:37 PM

    That is a lot more than I would’ve expected. I find that to be true about compound interest as well. It’s crazy how fast money (or numbers) grow when adding or multiplying them.

    1. J. Money April 16, 2013 at 6:23 PM

      I know right? It can slowly go AGAINST your favor too when applied to debt, ugh…

  12. Nick @ April 16, 2013 at 6:45 PM

    Also, we are kind of doing this with my daughter’s savings. We are giving her money for her birthday each year, $100 for every year old that she is. So last year we gave her $100, this year $200, etc. I’m pretty excited about it. It is $17,100 by her 18th birthday if I used your formula correctly.

    1. J. Money April 17, 2013 at 9:06 PM

      Woah! That’s gonna add up fast!

  13. stephanie April 16, 2013 at 10:00 PM

    lovin’ the math war-i’d have thrown in the white towel of surrender already! coffee or not, this is not a discussion i can enter. :-) however…i am adhering to the 1-2-3-4 up to $1300 by the end of the year. it’s not all that difficult and i like the way i’ve stretched a bit from week 1 and its $1 to this week, which is about $15. bit by bit, my little savings is growing and it makes me feel GREAT!

    1. J. Money April 17, 2013 at 9:07 PM

      Awesome! It should make you feel good so you can keep being motivated and continue pouring that money into your savings :) Way to go!

  14. Eric Poulin April 16, 2013 at 10:47 PM

    I always figure out those type of questions this way.
    1 + 365 = 366
    2 + 364 = 366
    3 + 363 = 366
    etc… until you get to the middle, leaving 183 by itself… so that’s 365/2 matches (182 matches totaling 366) + the leftover 183.
    = (floor(365/2) x 366) + 183
    = 66,612 + 183
    = 66,795.
    Ya… I’m a math geek too.

    1. J. Money April 17, 2013 at 9:08 PM

      Holy that gives me a head ache, haha… Good for you on being smart though :)

    2. Søren Seeberg January 4, 2018 at 9:00 AM

      Alternatively you could just:

      ceil(365 / 2) * 365 = 66.795

      However, this doesn’t work for even numbers :( I wrote this small Python program that can handle both even and odd numbers and compares against the result from the accumulation approach:

      x = 0
      z = 365
      # z = 14

      # By accumulation
      for y in range(1, z + 1):
      x += y

      print(‘Accumulated result : %s’ % x)

      # By calculation
      if z % 2 == 0:
      # Even numbers
      print(‘Calculated result(Even): %s’ % (math.floor(z / 2) * (z + 1)))
      # Odd numbers
      print(‘Calculated result(Odd) : %s’ % (math.ceil(z / 2) * z))

  15. Crystal April 16, 2013 at 11:28 PM

    Glad you figured out the total before you started the giveaways, lol! I really love that 52 week challenge. We are trying to go back to living on 50% of what we make (living on like 75% right now I think). Thanks for some learnin’ today. ;-)

    1. J. Money April 17, 2013 at 9:08 PM

      50% is an awesome number – I’d love to join you there again soon too!

  16. Elvin Peria April 17, 2013 at 12:51 AM

    Nice post J, you keep me glued on doing some math today. Anyway, I like the idea of 52 week challenge. I think I’m going to try that.

    1. J. Money April 17, 2013 at 9:15 PM

      Sweet man, go for it! I think it’s a great one too :)

  17. Shafi April 17, 2013 at 2:26 AM

    If you earn one penny today and tomorrow 2 pennies and third day 4 pennies and everyday you make double the previous day, you would be a millionaire by the end of the month.

  18. Nikita April 19, 2013 at 2:28 PM

    The 52 Weeks Savings Challenge is a cool idea! The obstacle I came across though was the feeling of sacrifice, which was good and bad: every time I made a transfer I felt proud of myself, but I found it hard to save consistently, especially as the weeks went by and the numbers went up! I think this is because of struggling with “the endowment effect”…( I felt like my money was “mine” and putting it aside felt like losing it. I think that feeling of sacrificing can gradually wear down your inspiration.

    Personally, I’ve developed three simple principles for easy saving. It should be regular (weekly is fine, daily is even better!), automatic (to not have to struggle with myself every time I save) and small (so as not to impact my day-to-day purchasing habits). I prefer saving like this because I only notice it when I see my savings account growing!

  19. J. Money April 20, 2013 at 10:14 AM

    I can understand that a bit. Felt the same way with my 401k starting out, but once it started accumulating to $1,000 and then $10,000 and then $50,000 I was like “go me! keep pumping it in!!” haha… but before I saw any real growth it was a tough one.

  20. jj549444 July 17, 2015 at 11:24 AM

    What is the formula???

  21. Marlen January 26, 2016 at 10:09 PM

    What’s the 100 for?? I want to do the 52 week challenge. How do I know how to substitute that info for this info?

    1. J. Money February 1, 2016 at 11:51 AM

      Not sure what you mean exactly, but def. encourage you to try the 52 week challenge :) Good thing is that you can start it anytime you want! And the money adds up fast, as you can see from some of the examples here.

  22. Julia June 8, 2017 at 10:10 AM

    Thanks for the info here!
    I’m also interested in attempting the 52 week savings challenge :)

    The only issue I have with this is the image at the top, that formula is written incorrectly. Surprised no other math whizzes picked up on it!

    1. J. Money June 11, 2017 at 2:38 PM

      Hah! Yeah – need those parenthesis around that first part huh :)

    2. Gaz November 15, 2017 at 7:07 PM

      This is how I arrive at the answer. Lets do 1-10 first. Take the last number in sequence e.g. number 10. Divide this by 2 = 5. Multiply this by the last number = 50 and then add the 5. So the sequence will add up to 55. So to recap 10/2 x 10 + 5 = 55.
      Now for 1-365 adding 1 everyday of the year. So last number is 365/2 = 182.5
      So 365×182.5 + 182.5 = £66,795