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## Homework Statement

Expand [tex](1-3x)^{\frac{1}{3}}[/tex] in ascending power of x , up to the term x^3 . By using an appropriate substitution for x , show that [tex]\sqrt[3]3=\frac{33809}{19683}[/tex]

## Homework Equations

## The Attempt at a Solution

the expansion would be 1-x-x^2-(5/3)x^3 and the range of x whixh make this expansion valid is |-3x|<1/3 .

My question is how do i find this appropriate substitution for x ? Instead the guessing way , is there a proper way ?