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

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In summary, the conversation discusses the sum of integers from 1 to n, which can be expressed as n(n+1)/2. The equations n(n+2)/2 = r(r+1) and m(m+1)/2 = 20/r are mentioned, with the only solution being n = 3, m = 4, and r = 2. The speaker is uncertain if they understood the problem correctly.
  • #1
tharindhudg
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sum of 1 n = 20/ r = 1
r(r+1)
 
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  • #2
tharindhudg said:
sum of 1 n = 20/ r = 1
r(r+1)

It would help if you could clarify your expression.
 
  • #3
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
 
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  • #4
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.
 
  • #5
This topic made me laugh for some reason.
 
  • #6
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.
 

1. What is the formula for calculating the sum of 1 to n with r = 1?

The formula for calculating the sum of 1 to n with r = 1 is n(n+1)/2.

2. How do you derive the formula for the sum of 1 to n with r = 1?

The formula for the sum of 1 to n with r = 1 can be derived using the method of mathematical induction.

3. What is the significance of r = 1 in the sum of 1 to n formula?

The value of r = 1 in the sum of 1 to n formula represents the common difference between consecutive terms in the arithmetic progression.

4. Can the formula for the sum of 1 to n with r = 1 be used for other values of r?

No, the formula for the sum of 1 to n with r = 1 is specifically designed for the case where r = 1. For other values of r, the formula would be different.

5. What are some real-life applications of the sum of 1 to n with r = 1 formula?

The sum of 1 to n with r = 1 formula is commonly used in various fields such as mathematics, physics, and computer science. It is used in calculating the total number of objects in a sequence, finding the area under a curve, and in algorithms for sorting and searching data.

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