hi im new here and not very good with math terms of english words
i have this to make and i just dont know how i tried but it just wouldnt happen
Write (find) the first 3 terms in binomianl series to calculate approximate value for n-th root ; n=3.
28^(1/n) ?
thx in advanced
Hello, Paps!
Welcome aboard!
Find the first 3 terms in binomianl series to calculate approximate value of:
The binomial series looks like this:
^n\;=\;a^n + n\!\cdot\!a^{n-1}b + \frac{n(n-1)}{2!}a^{n-2}b^2 \,+)
We have: .. . . where:
The first three terms are: .
. .![= \;\sqrt[3]{27} + \frac{1}{3(\sqrt[3]{27})^2} + \frac{\frac{1}{3}(-\frac{2}{3})}{2(\sqrt[3]{27})^5} \;=](http://latex.codecogs.com/png.latex?= \;\sqrt[3]{27} + \frac{1}{3(\sqrt[3]{27})^2} + \frac{\frac{1}{3}(-\frac{2}{3})}{2(\sqrt[3]{27})^5} \;=)
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
This is a very good approximation!
The actual value is: .
Our answer gives us: .
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