The Natural Logarithm and its Series Expansion - 2 Ways [ ln(x+1) at 0 ]

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We are once again back with taylor series expansions! =) Today we are going to deal with ln(1+x) at 0. We are going to do it in two ways, one is the regular way and the other one is by using integration of the geometric series. Enjoy! =)

[tatjanagobold]

Flammy, this day was quite shitty for me due to terrible recurring migraines, but this video lifted me out of bed because I just love series expansions and all your videos in general <3 have a flammy weekend ^^

[SuperMiketron]

Finally a video I can understand myself and not feel like a dumbass. Thanks papa!

[officialEricBG]

We literally did this in lectures today, the lecturer had the old way in his notes but he also just went your way :D

[sichelsam]

I usually watch these because youre th meme Lord but this time it helped me actually, thank you for being so amazing papa flammy 😍

[luchisevera]

Why do they call it a natural log if there are no trees to be seen? HmMmMmM...

[abdullasulfikkar]

I just don't know what to comment 😂😂😂😂😂😂 .Keep it flaming

[atrimandal]

Another series expansion! Thanks papa❤️

[nontrivialdog]

I just used this to obtain the perturbative expansion of the free energy of a weakly interacting fermi gas!

[tobiasguivarch]

I think you missed to put the minus sign in front of the sum symbol on the thumbnail...

[tytuer]

Logarithm function annoys me. It has no power series that converges for real numbers, ( if there is, I do not know) also, I could not find such a function f(x), that is not a logarithm and satisfies lim(x->inf)f(x)=inf and lim(x->inf)(f(x)/lnx)=0.

Why do I bother myself with these? I am just an engineer. Let's take π=3. Lolz

[korayacar]

1:29
It‘s the negative _first_ power, if you‘re curious.
edit: timestamp

[willnewman]

Why are you indexing over prime ideals?

[okoyoso]

That reminds me. Any progress on that lnx = f(x) + lnf(x) problem?

[MurtadhaAljanabi]

Can't we just use uniform convergence of power series to justify interchanging the sum and the integral?

[josueantonio]

How to Integrate ( x^2sec^4(x) ) ???
Help pls!!