Can someone tell me how this equals 3 please, using Taylors expansion?

Can someone tell me how this equals 3 please, using Taylors expansion?

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How's calc 2 treating you?

Doing me dirty

How did it treat you

I feel you. Calc 2 stuff could be a bitch sometimes. I wish I remembered more about Taylor Series off the top of my head. Have you looked for an answer on Slader? They've got every book answer with steps if you use one of Stewart's textbooks.

ahh he doesn't use a textbook, only his own typed notes

where did u study bro

been on this shit for hours

I took it at UCCS. I looked through my old notes but I doubt they'd help here

ohh thats cool im down at Bristol Uk

nigga. if this is hurting you, god help you in calc 3. holy fuck. you're fucked to the nth degree.

bro nahhh this simpllification is fucking hard

i can split them into two seperate sums but then i get some bad shit

Maybe, maybe not. I'm finishing Calc 3 now and I don't remember shit about series. It's all about partial derivatives and multiple integrals and vectors and such. I haven't even used the word "series" since calc 2. Got a 90% on my last exam, by the way.

It’s a bit of a dead topic

Have you tried turning this into a function of x, splitting the x integral up and deriving the numerator. Multiplying by its reciprocal and then churn out values that approach 3

Also this maclaurin because n starts at 0

6 * sum_n (-1)^n*(pi/6)^{2n+1}/(2n+1)!
= 6 * sin(pi/6) = 6 * (1/2) = 3
someone said this but i dont get how to factor out the 6

taylor series n also starts at 0 retard

you gotta remember your taylor expansions, then try to manipulate your function to look like it

got the right idea

sin x = x - x^3/3! + x^5/5! - ...

now look at what you've got. what does the x look like?

top (ignoring the -1) is pi * pi^2n (factoring out one pi)
bottom is 6^2n (ignore factorial for now)

if you combine you have pi * ((pi/6)^2)^n

Oh no it’s retarded.

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ohh i get that, but why is it times 6

ohh clocked it

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they did it differently, and my math is wrong

instead of trying to make the powers (2x-1) I tried to make them 2x and factored out a pi on top
he factored in a 6 to make it 2x-1

moral: check your summation indexes!