Series

[marble zodiac]

Help

Does the middle part equal to

$1-1+1-(-x^2/2)+1-(x^4/24)$

[lime rover]

ЖѲTЇЇC

[marble zodiac]

$2+(x^2/2)-(x^4/24)$

[lime rover]

ЖѲTЇЇC

[marble zodiac]

.

[ivory summit]

what isthe question exactly

[marble zodiac]

I’ll send a picture

[ivory summit]

oh i see

[marble zodiac]

It’s the question 5

I’m currently trying to work out 1-cosx

[ivory summit]

i see

1-cosx is $$\sum_{n\ge1} (-1)^{n+1}\frac{x^{2n}}{2n!}$$

[lime rover]

icebear

[marble zodiac]

Do I plug that into the bottom?

And I can use r instead of n right like the top one

[ivory summit]

yes

[marble zodiac]

Then does it simplify down?

Cause I need to prove that it is equal to 2/3

As it gets closer to 0

[ivory summit]

oh youre doing the limit

[marble zodiac]

Yes I’ve got to prove as x gets closer to 0 it is equal to 2/3

But it’s mainly all about series on the sheet

[ivory summit]

i see

well you gotta cancel out some xs

x's

[marble zodiac]

He did an example on the board where everything was divisible by x^2

So then it all cancelled down

[ivory summit]

yea

[marble zodiac]

And then am I able to basically just ignore anything with an x because they r basically 0?

[ivory summit]

yep

[marble zodiac]

Ok thank you

[ivory summit]

tell me what you obtained with numerator

[marble zodiac]

I can’t work on it rn

[marble zodiac]

Wym

[ivory summit]

what series did u obtain with numerator

[marble zodiac]

Should be this right?

I also still have to prove that the top part of the thing I showed you is equal to that

[ivory summit]

yes

now after factoring the x^2 out from both series what do u get

[marble zodiac]

Give me a min have to do something else rq

[ivory summit]

same i gtg now too

but i think you got this now

for convenience

you can only consider the first 3 terms of each series

[marble zodiac]

Ok tyvm