- #1
isukatphysics69
- 453
- 8
I don't understand something, the sum n=1 until infinity of (1/n) is a divergent harmonic series meaning that its sum is infinite right?
After reading that i started thinking about the finite volume of the function (1/x) being revolved around the x-axis referred to as "Gabriels horn". They say that the area is getting so small as x -> infinity and that makes the volume finite after being revolved. Now they are saying that the sum of (1/n) from 1 to infinity is divergent, so they are taking these tiny fractions and summing them and saying that the sum will be infinite, that seems like it contradicts what they said about the finite volume. They are saying that an infinite amount of very small fractions will sum to infinity, but the very small area of 1/x as x-> infinity being revolved around the x-axis is going to produce a finite volume. Really confused here
After reading that i started thinking about the finite volume of the function (1/x) being revolved around the x-axis referred to as "Gabriels horn". They say that the area is getting so small as x -> infinity and that makes the volume finite after being revolved. Now they are saying that the sum of (1/n) from 1 to infinity is divergent, so they are taking these tiny fractions and summing them and saying that the sum will be infinite, that seems like it contradicts what they said about the finite volume. They are saying that an infinite amount of very small fractions will sum to infinity, but the very small area of 1/x as x-> infinity being revolved around the x-axis is going to produce a finite volume. Really confused here