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In the last two steps of the derivation for the formula to determine the surface area of revolution the infinite sum of frustums converges to give the integral. (for a visual representation of what i'm saying pls click here: https://drive.google.com/file/d/147Qf-FfSYBS_DtmPkCaKzfnZt44CmCSl/view?usp=sharing )

However, how do you explain why the infinite series (the sum of the SA of frustums as the number of frustums approaches infinity) converges and not diverges? Tried using the ratio test but it showed that the sequence diverges, which is incorrect because when i plug values in I get a finite value for area.

Found something on math stack exchange How to prove the arc length of smooth curve converges to the straight length? but its a bit complicated for me (a high school student) to understand

cdlc2005
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  • How did you apply the ratio test here? There is no infinite series anywhere in sight. You can find some information about writing the formulas here: http://math.stackexchange.com/help/notation (this markup is not exactly unique to stackexchange, it's also very useful for writing math papers). – David K Mar 19 '23 at 15:45
  • To be specific, what you have is actually an infinite sequence in which each term is a finite series. The sum is only conceptually infinite due to taking the limit. – David K Mar 19 '23 at 16:13

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