The Student Room Group

Binomial expansion

Hey I'm having trouble expanding (1+x^3)^1/2 would you please help me with expanding with fractional powers
Reply 1
Original post by Sele Damison
Hey I'm having trouble expanding (1+x^3)^1/2 would you please help me with expanding with fractional powers

You should have done the infinite series for
(1+x)^(1/2)
so just do the same with the "x" replaced by "x^3". Upload what youve tried if you get stuck.
I'm sorry but how do we even expand the infinite series (1+x)^1/2
Reply 3
Original post by Sele Damison
I'm sorry but how do we even expand the infinite series (1+x)^1/2

You should have covered it if youre expected to answer the question (is it a level?) but
https://mmerevise.co.uk/a-level-maths-revision/infinite-series-binomial-expansions/
If you have learned Maclaurin series (I suspect not, but alas, extra knowledge!), it's the same thing.
f(x)=k=0f(k)(0)xkk!\displaystyle f(x) = \sum_{k=0}^\infty \frac{f^{(k)}(0)x^k}{k!}
Plug in f(x) to be your binomial and you're good to go.

And this is especially nice for real powers of x, since power rule is easy.
(edited 1 month ago)
I get it now! Thank you

Quick Reply