How to Find the Maclaurin series of 1/(1-x)

In this video I will teach you how to derive the Maclaurin series of 1/(1-x) in a step by step tutorial. This is one of the most useful Maclaurin series as it can be used to derive many other series.

[AnnieMcCutcheon]

Thank you so much! I've had a mental block on power series since my Calc BC class senior year, and this video helped more than anything!

[morganga]

Working backwards, you can treat the power sum as a geometric series, then the formula for the first n terms is 1(1 - x^n) / (1 - x). Taking limits as n -> infinity, x^n -> 0 when |x| < 1, so sum = 1/(1-x).

[prettymuchanobody]

I know I'm a bit late to the party but why does this only work for 0<x<1?
I mean it obviously doesn't work outside of this interval but mathematically speaking, what step did we apply that restricts us to this interval?

[_odyssey_____]

What is the general form of nth derivative of f(x) here..?

[BrenoMeireles]

Valeu, daqui do Brasil vi seu vídeo e me ajudou muito. Like!

[kaiz]

Thanks for your nice video :) but I am not sure if the remainder part O(x^5) is correct, I think it might be O(x^4) since lim_{x→0} remainder(x) / x^4 is 0, but this equation might not be correct when the denominator is x^5.

[pardiskhodakarami]

so helpful! please upload more lessons.

[nathanschwedock]

what accent do you have? I can't tell and it's driving me nuts