I'm not understanding |x| < 1.
I understand that if the expansion is an infinite series then it needs to converge but then shouldn't it be |1 + x| < 1? Help.
#binomial expansion (infinite series)
shell shale
latent oasisBOT
ivory kiln
I'm not understanding `|x| < 1`.
I understand that if the expansion is an infin...
If $1 \le \abs{x}$ the sum will diverges to infinty
because $\lim_{n \to\infty} C_n^k x^n \neq 0$
where $C_n^k$ is a binomial coefficient
latent fractalBOT
un_decorateur
shell shale
simpler terms pls
civic tendon
I'm not understanding `|x| < 1`.
I understand that if the expansion is an infin...
They say that cause if mod x is less than 1 it keeps decreasing for higher powers and will eventually tend to zero
So you can approximate the value
Using binomial expansion
civic tendon
I'm not understanding `|x| < 1`.
I understand that if the expansion is an infin...
Have you learnt PNC and binomial theorem?
ivory kiln
simpler terms pls
the binomial coefficient are the
$\frac{n(n-1)}{2}, \frac{n(n-1)(n-2)}{3!}$
which come from binomial expansion of $(1+x)^n$
the guys in front of the $ x^2, x^3$
and I say that if $1 \le \abs{x} $
the sum diverges because the terms didn't converge to 0
latent fractalBOT
un_decorateur
shell shale
Have you learnt PNC and binomial theorem?
what did you mean by PNC
civic tendon
Permutations and combinations
shell shale
i don't know what that means and in not sure if i call it something different but I've learned binomial theorem
civic tendon
Right then do you know how to expand x+1 to the power n in general?
shell shale
I've finished the a level maths course (UK)
so UK college
which is 16-18 age
this is from a level maths
shell shale
Right then do you know how to expand x+1 to the power n in general?
yeah
i know for positive integers and for fractional/negative powers
but im not getting the domain for x
civic tendon
i recognise this but not npr
Right this combination,so basically a+b whole square etc is from this
civic tendon
which is 16-18 age
I’m from India so we learn this at like age 16
civic tendon
Right this combination,so basically a+b whole square etc is from this
Do you know what an infinite geometric progression is?
I can try to explain it to you
shell shale
They say that cause if mod x is less than 1 it keeps decreasing for higher power...
im confused cuz if |x| < 1 then the highest number that could be in the bracket is 1.99999999.... so (1.9999999)^n
then in my eyes wouldn't it be divergent
cuz i thought the thing inside the brackets has to be between -1 and 1 exclusive
civic tendon
im confused cuz if |x| < 1 then the highest number that could be in the bracket ...
Yeah but that number to a really high power is very close to 1
So you’re right the first few terms are not negligible but as the power keeps increasing using the formula ncr(1)(x)^r
When r is big it tends to zero
So the whole term is very close to 0
shell shale
i typed 1.999^20 in my calc and it gives 1038139.898 so if the number keeps getting to large numbers like this wouldn't it be diverging instead
oh wait
ohhhhhhh
civic tendon
So the whole term is very close to 0
Does that make sense?
shell shale
i get it
civic tendon
Rightttt
civic tendon
Yeah
shell shale
it took way too long 😭
civic tendon
Do you know where’s to find what I answered bed
Bef*
Cause I answered a probability question somewhere
civic tendon
it took way too long 😭
I mean at least you got it now
shell shale
Do you know what an infinite geometric progression is?
i know a geometric progression uses the formula nth term = ar^(n-1)
civic tendon
i know a geometric progression uses the formula nth term = ar^(n-1)
Aaah that’s not right do you mean a(r^n-1)/r-1
shell shale
Aaah that’s not right do you mean a(r^n-1)/r-1
that's to find the sum of n number of terms
civic tendon
Aaah that’s not right do you mean a(r^n-1)/r-1
Anyway I just wanted to say when the common ratio is less than 1 we take the numerator to be just a
civic tendon
that's to find the sum of n number of terms
Yeah shit I’m sorry did I not say sum?
shell shale
icic