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_Mayday_
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Hey, I've been trying to work this out for a few days now. There is supposed to be an easy way to add all the numbers from 1 to 100 easily, anyone know?
_Mayday_ said:Brilliant cheers. I thought it had something to do with that but I struggled to put it into a formula.
_Mayday_ said:Hey, I've been trying to work this out for a few days now. There is supposed to be an easy way to add all the numbers from 1 to 100 easily, anyone know?
country boy said:There is another way to visualize this using square arrays of elements. In a square array that is m=n+1 elements on a side, the number of off-diagonal elements in the lower left (or upper right) is (m^2-m)/2. But this is also the sum of the number of elements in all of the rows in that part of the matrix: 1+2+3+...+n. In our case n=100, m=101 and (m^2-m)/2=5050. This is equivalent to the Werg22 and Curvation solution.
To get K.J.Healey's solution, note that if we subtract half of the off-diagonal elements (say the upper right) in an nxn array then the remaining number of elements is n^2-(n^2-n)/2=(n^2+n)/2, again the sum of rows is 1+2+3+...+n. But this is n*(n/2)+(n/2) and is equal to 100*50+50 in our case.
Putting m=n+1 into (m^2-m)/2 gives (n^2+n)/2, so the two array visualizations are equivalent, of course.
[tex]\sum_{n=1}^{100}1+\frac{1}{n}=\sum_{n=1}^{100}1+\sum_{n=1}^{100}\frac{1}{n}[/tex]Alex48674 said:I know how to do this but how would you do it if it weren't just intigers like 1 to n. What if you wanted to add 1+1/n where n = a positive intiger? let's say where n is 1 to 100
Gokul43201 said:[tex]\sum_{n=1}^{100}1+\frac{1}{n}=\sum_{n=1}^{100}1+\sum_{n=1}^{100}\frac{1}{n}[/tex]
[tex]~~~~~=100+ \sum_{n=1}^{100}\frac{1}{n}[/tex]
The remaining term above is a partial sum of a harmonic series. There is no simple, closed-form expression for such a partial sum to arbitrary number of terms. I think there are "compact expressions" for small partial sums and approximations for large ones, but that's all.
_Mayday_ said:Hey, I've been trying to work this out for a few days now. There is supposed to be an easy way to add all the numbers from 1 to 100 easily, anyone know?
In other words the number you are adding times the next highest number divided by 2 = answerJ R said:100 X 101 divided by 2 = answer. All numbers work the same. 50 x 51 divided by 2
44 x 45 divided by 2 10 x 11 divided by 2
Schrodinger's Dog said:Incidentally there's a famous story where Gauss was asked this in a maths class at the age of 7, thinking to stump the children; Gauss gave him an immediate answer, something like the above answers given by the others, by figuring the above simple relation.
Alex48674 said:I know how to do this but how would you do it if it weren't just intigers like 1 to n. What if you wanted to add 1+1/n where n = a positive intiger? let's say where n is 1 to 100
Werg22 said:There's also the approximation [tex]log(100) + {\gamma}[/tex]
With [tex]{\gamma} = 0.577215665...[/tex]
I wonder if it's possible to measure the order of magnitude of the error.
Werg22 said:There's also the approximation [tex]log(100) + {\gamma}[/tex]
With [tex]{\gamma} = 0.577215665...[/tex]
I wonder if it's possible to measure the order of magnitude of the error.
NightGale said:Consider using arithmetic progression's formula:
n/2(a+n) where a is the 1st term = 1, and n is the number of terms = 100
Air said:1+100=101, 2+99=101, 3+98=101 etc. There are 50 pairs of these so it is 101 times 50 which equals 5050.
The formula for adding the numbers from 1 to 100 is (n * (n+1)) / 2, where n is the highest number in the range (in this case, 100).
Yes, you can use a calculator to add the numbers from 1 to 100. Simply enter the formula (n * (n+1)) / 2, where n is 100, and the calculator will give you the answer.
Yes, there is an easier way to add the numbers from 1 to 100. You can use the Gauss's method, which involves pairing the numbers from the beginning and end of the range and multiplying them by the total number of pairs (in this case, 50 pairs).
Knowing how to add the numbers from 1 to 100 is important because it helps develop mathematical skills, such as understanding patterns and formulas, and it can also be used in various real-life situations, such as calculating the total cost of a large number of items.
Yes, there are other mathematical methods that can be used to add the numbers from 1 to 100, such as using a spreadsheet or writing a computer program. However, the formula method and Gauss's method are the most commonly used and efficient methods for adding numbers in a range.