Find
#binomial expansions
vivid carbon
paper pine
Find
jus do the specific term(s) that would get you to x²
and then compare coefficients
it's gonna go 10, 8, 6, 4, 2, 0
crystal bison
this is so embarrassing im cooked
indigo willow
10C what 🧏♂️
vivid carbon
10C what 🧏♂️
5?
crystal bison
10C what 🧏♂️
go play roblox
crystal bison
L
indigo willow
Ikr
vivid carbon
it's gonna go 10, 8, 6, 4, 2, 0
The coefficients?
indigo willow
,w 10C6
gilded needleBOT
indigo willow
,w expand(x + 1/x)^10
paper pine
Wait how did you get that
use the formula
gilded needleBOT
indigo willow
It is 10C6
indigo willow
Oh is that symemtiacla
paper pine
something in the form (x+1/x)^n where n is even will give you even powers decreasing
indigo willow
that gives u the x^-2 co-efficient
What
vivid carbon
use the formula
the one with factorials?
paper pine
the one with factorials?
u can use that one if u want
it'll probably be easier for this q actually
or
just use ur brain
indigo willow
that gives u the x^-2 co-efficient
No it would be 10C6 x^6 * (1/x)^4
lavish sage
No it would be 10C6 x^6 * (1/x)^4
other way round
if u do 10C6 u get x^4 * (1/x)^6
giving u x^-2
gilded needleBOT
lavish sage
yes
indigo willow
I never use ncr in binomial expansion I wasconfusing myself
lavish sage
this ones a bit harder to do just straight up, but just straight up substituting into the binomial series makes it alot simpler
[(x+x^{-1})^{10} = \sum_{k=0}^{10} \binom{10}{k} x^{10-2k}]
10-2k = 2 \
k = 4 \
So we calculate:
[\binom{10}{4} (x^6) \left( \frac{1}{x} \right)^4 = 210 x^2]