Cutting Tape - Application of Geometric Series

In this video I demonstrate how to use formulas for the summation of a geometric series to calculate the length of tape is required if I was to cut it first by 10cm, then 96% of that, then 96% of the previous cut and so on.

I first calculate how much tape is required for 10 cuts, then I calculate how much is required for any number of cuts.

So to work out how much tape is required, we can add up the first few cuts to see if there is a pattern or progression.

To make 1 cut: we need 10cm.

To make 2 cuts: we require 10cm, plus an additional 0.96×10cm of tape.

To make 3 cuts: we require an additional 0.96×0.96×10cm

So adding all of these together we get...

10 + 10×0.96 + 10×0.96×96 + ... = 10×[1 + 0.96 + 0.96² + 0.96³ +...]

This is a convergent geometric series for which we can find the sum of n-terms and summation to infinity.