What is the sum of integers from 1 to n with r = 1 if n = 20?

  • Thread starter Thread starter tharindhudg
  • Start date Start date
  • Tags Tags
    Sum
AI Thread Summary
The discussion revolves around calculating the sum of integers from 1 to n, specifically when n equals 20 and r equals 1. The correct formula for this sum is n(n+1)/2, leading to a total of 210 for n = 20. Participants express confusion regarding the role of r in the equation, with some interpreting it as a variable in a diophantine equation. The only solution derived from this interpretation is n = 3, m = 4, and r = 2, though there is uncertainty about the problem's original intent. Overall, the main focus is on clarifying the sum of integers and the relevance of r in the context of the problem.
tharindhudg
Messages
1
Reaction score
0
sum of 1 n = 20/ r = 1
r(r+1)
 
Physics news on Phys.org
tharindhudg said:
sum of 1 n = 20/ r = 1
r(r+1)

It would help if you could clarify your expression.
 
tharindhudg said:
sum of 1 n = 20/ r = 1
r(r+1)

If construed as a number theory problem, the best that I could come up with

sum of 1 to n = r(r+1) sum of 1 to 3 = 2*3 etc.
sum of 1 to n = 20/r sum of 1 to 4 = 20/2
So r = 2
 
Last edited:
If I understand you correctly, you are summing the integers from 1 to n.
This sum is n(n+1)/2. I have no idea what you mean by r.
 
This topic made me laugh for some reason.
 
mathman said:
If I understand you correctly, you are summing the integers from 1 to n.
This sum is n(n+1)/2. I have no idea what you mean by r.

I viewed it as two diophantine equations in two variables

n(n+2)/2 = r(r+1) and m(m+1)/2 = 20/r for which the only solution is n = 3, m =4, r = 2

I did not use the formula n(n+1)/2 since I knew the values of n(3) and n(4) already.

No certainty that I understood the problem correctly though I don't see how there could be a different problem intended.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Find the sum of the coefficients in the expansion ##(1+x)^n##
Replies
5
Views
2K
Show that ##^{n+1}C_r=^nC_r+^nC_{r-1}##
Replies
14
Views
2K
Every integer greater than 5 is the sum of three primes?
Replies
4
Views
3K
Find the ##r^{th}## term of ##(a+2x)^n##
Replies
3
Views
2K
Find the ##r^{th}## term from beginning and end of ##(a+2x)^n##
Replies
13
Views
1K
Where Did ##(n−r+1)^{th}## Come From in Binomial Expansion?
Replies
3
Views
1K
Prove that the integers ## c, c+a, c+2a, c+3a, ...., c+(n-1)a ## ....
Replies
6
Views
1K
Determine all integers ## n ##
Replies
10
Views
1K
For n>3, show that the integers n, n+2, n+4 cannot all be prime
Replies
27
Views
3K
Determine all integers ## n ## for which ## \phi(n)=16 ##
Replies
14
Views
2K

Hot Threads

Recent Insights

Back
Top