♾ Stop memorizing! Proving the formula for the sum of an infinite geometric series… kind of ♾
Автор: 20circles
Загружено: 2022-10-08
Просмотров: 345
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Yup, you already knew this was coming! Since we worked with numbers last time, we have to generalize with letters and derive the formula for the sum of an infinite geometric series… sort of? We go through the exact same steps like we did with our numbers, but the restriction is where things get a little bit trickier. This is why it deserves special attention in its own little video, hence the “sort of” because the proof isn’t exactly complete yet.
To show why the magnitude (absolute value) of the common ratio must be less than 1, we first need to get familiar with the idea of convergence/divergence. But feel free to play around before I present this topic by changing values of the common ratio and observing what happens to the infinite geometric series. For example, try a = 5, and compare r = 10 vs r = 1/10. Try computing a few sums (first term, first two terms, first three terms, etc). Notice anything interesting?
CREDITS
Equipment:
Camera: iPhone XR
Microphone: Blue Yeti X
Editing Software: Davinci Resolve 18
Outro Song:
Track: Ikson - Do It [Official]
Music provided by Ikson®
Listen: • #90 Do It (Official)
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