Sum of all numbers between A and B

[Deleted member 4993]

Fun Idea Mrspi.


Sum of all numbers between A and B (both same sign) is infinite,
HOWEVER, the average of all numbers between A and B (both same sign) is finite,
Challenge: Can anyone calculate the Geometric mean of all numbers between 0 and 1?

Is that 0<R≤1

or

0≤R≤1

 

[Bob Brown MSEE]

Geometric mean of all numbers between 0 and 1?

Geometric mean of all numbers between 0 and 1
0<R<1

 

[lookagain]

Geometric mean of all numbers between 0 and 1
0<R<1

\(\displaystyle \boxed{ \ \dfrac{1}{e} \ }\)



\(\displaystyle \displaystyle\lim_{n\to\infty}\bigg(\dfrac{\sqrt[n]{n!}}{n}\bigg)\)

 

[mackdaddy]

I'm VERY surprised that no one commented on the part of the original post (and also quoted in numerous responses) which said "the sum of all numbers between A and B". The original posted then proceeded to deal with an example where A = 2 and B = 6, which handled the numbers 3, 4, and 5. There are INFINITELY many numbers between 2 and 6, such as 2.75, 3.1010010001......, pi, 9/2, etc.

I think you need to re-phrase your statement to say "all whole numbers between A and B."

Otherwise, I am impressed with the depth of thought and comprehension displayed by a 9th grader here! Congratulations!

thank you very much! Your coment is greatly appreciated! Also I wanted point out something Irealized just yesterday. The sum of all whole numbers 1 through n-1 equals the maximum intersections made by n lines. I would go on and show you how the formulas are the same but im writing this on my xbox!

 

[Bob Brown MSEE]

Correct!

\(\displaystyle \boxed{ \ \dfrac{1}{e} \ }\)



\(\displaystyle \displaystyle\lim_{n\to\infty}\bigg(\dfrac{\sqrt[n]{n!}}{n}\bigg)\)

Kudos to lookagain!