Binomial Series

**TreePerson** · Mar 28th 2010, 01:34 PM

Use the binomial series to get a 3 term series for (2+4rootx)^3 and find the valid values for x.

What do u do with the 2?

**Deadstar** · Mar 28th 2010, 04:03 PM

Ok. You gotta change it to the form $(1+x)^n$ so...

$(2 + 4 \sqrt{x})^2 = (2(1 + 2\sqrt{x}))^3 = 2^3 (1+2\sqrt{x})^3$

Then plug this into the binomial series which is...

$(1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \dots$

With $n=3$ and $x=2\sqrt{x}$ .

The binomial series is valid when $|x|<1$ so find $x$ such that $|2\sqrt{x}|<1$

**TreePerson** · Apr 16th 2010, 09:32 PM

Thanks ALOT, sorry for late reply...

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