Expand (1+x)^-1/4 in ascending powers of x up to the term in x^2.
Prove that 3/2(1+1/80)^-1/4=5^1/4.
Using your expansion for (1+x)^-1/4 and x=1/80,find an approximation for 5^1/4, giving yr answer correct to 5d.p.

Question

Expand (1+x)^-1/4 in ascending powers of x up to the term in x^2.
Prove that 3/2(1+1/80)^-1/4=5^1/4.
Using your expansion for (1+x)^-1/4 and x=1/80,find an approximation for 5^1/4, giving yr answer correct to 5d.p.

eric_d · Answer

@ganeshie8

eric_d · Answer

@ikram002p

ikram002p · Answer

hehe i will try what ganesh did in the previouse qn 
else i have no idea :P

eric_d · Answer

ok

ganeshie8 · Answer

yeah binomial expansion again

ganeshie8 · Answer

start by writing out the binomial expansion formula

ganeshie8 · Answer

$$\large \begin{align}
 (x+1)^{-1/4} &= \sum \limits_{k=0}^{\infty }  \binom{-1/4}{k} x^r \ 
 &=\binom{-1/4}{0} x^0    +\binom{-1/4}{1} x^1  +\binom{-1/4}{2} x^2     + \cdots
\end{align}
$$

ganeshie8 · Answer

@ikram002p wana practice binomial expansion with fractions ? :)

ikram002p · Answer

yeah , but i have to go nw >.<
will you teach me this ?

ganeshie8 · Answer

really nothing much to teach you lol
you already know binomial expansion, so simply extend it to fractions and hope that it works, thats all :)

ikram002p · Answer

oki , ill try when i come back mmmm

eric_d · Answer

Thanks @ganeshie8

ganeshie8 · Answer

np :) have u finished it ?