Binominal Series: expand in ascending powers of X as far as x3: 1/sqrt{4+x}

Daz

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Good morning,

This is my first time on here and am completely stuck. Could someone help me with this question please? I genuinely have no one else to ask.

Thanks very much


Expand the following in ascending powers of X as far as the term in x3 using Binominal Series:

1
______
square root of (4+x)
 
Expand the following in ascending powers of X as far as the term in x3 using Binominal Series:

1
______
square root of (4+x)
What is the relationship between the two variables, X and x? What formulas or methods did they give you for this? How far have you gotten in applying this information?

Please be complete. Thank you! ;)
 
Good morning,

This is my first time on here and am completely stuck. Could someone help me with this question please? I genuinely have no one else to ask.

Thanks very much


Expand the following in ascending powers of X as far as the term in x3 using Binominal Series:

1
______
square root of (4+x)
Assuming you mean expand
\(\displaystyle \dfrac{1}{\sqrt{4+x}}\, =\, (4+x)^{-\, \dfrac{1}{2}}\),
what have you learned about expanding expressions such as this in a binomial series?

Hint: If we let u = \(\displaystyle \frac{x}{4}\), you might have an easier time with the expansion to start with when you re-write the term as 2*\(\displaystyle (1+u)^{-\frac{1}{2}}\). Also note that it doesn't matter whether the exponent, \(\displaystyle -\frac{1}{2}\) in this case, is an integer on not nor whether it is positive or negative, the same general form applies
\(\displaystyle (1+x)^n\, =\, 1\, +\, \dfrac{n-0}{1!}\, x\, +\, \dfrac{n\, (n-1)}{2!}\, x^2\, +\, \dfrac{n\, (n-1)\, (n-2)}{3!}\,\, x^3\) + ....
Also see
http://mathworld.wolfram.com/NegativeBinomialSeries.html
 
This Question requires manipulation of the given expression to match the ‘standard’ form of the binomial series before the expansion can be performed.

. Expand the following in ascending powers of x as far as the term in x3 using the Binomial Series:

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State the limits for which the expansion is valid.

This is the information i have and im struggling. Any help you can provide will be greatly recieved. Thank you alread for the support!!

Daz
 

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