<s>[INST] Binomial Expansion to Evaluate the Value of $\frac{1}{\sqrt{3.4}}$ I've found the binomial expansion of $\frac{1}{\sqrt{1+x}}$ to be
$1-\frac{1}{2}x+\frac{3}{8}x^2-\frac{5}{16}x^3+...$, but why does the series converge for $x=2.4$? Is it because $x>1$? 
So how can I otherwise evaluate the value of $\frac{1}{\sqrt{3.4}}$ using the binomial expansion?
 [/INST] You can use $\displaystyle\frac{1}{\sqrt{4+x}}=\frac{1}{2}\frac{1}{\sqrt{1+\frac{x}{4}}}=\frac{1}{2}\left(1+\frac{x}{4}\right)^{-1/2}$, so now 
you can
substitute $\frac{x}{4}$ for $x$ in your series, and then replace $x$ by -.6.
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