What is the Correct Way to Write a Binomial Expansion for (1+(1/x))^(-3/2)?

[bdolle]

<Moderator's note: Moved from a technical forum and therefore no template.>

Hey All,

For my modern physics class we were told to write out a binomial expansion of (1+(1/x))^(-3/2). I am fairly confident in the work I did, but my professor posted his work and it is different and way simpler than mine. Would love feedback.

My work is the second page (pencil and final answer in pen).

It looks like my professor simply took the binomial expansion of just (1+B)^(3/2) using B=(1/x) and forgot to take into account the minus sign on the exponent. Forgivable, but I don't think that is the right way to tackle this.

I algebraically manipulated (1+1/x) to get (1/x)(1+x). Then wanting to pull the term (1/x) out of the entire expansion I had to take it out of the (-2/3) power making it 1/(x^-3/2) which is x^(3/2). Then I took the expansion of (1+x)^(-3/2) and mutliplied it by my factor of (x^(3/2)).

Anyone care to take a crack at this?

THANKS!

 

[mjc123]

Post it the right way up please!

 

[Ray Vickson]

<Moderator's note: Moved from a technical forum and therefore no template.>

Hey All,

For my modern physics class we were told to write out a binomial expansion of (1+(1/x))^(-3/2). I am fairly confident in the work I did, but my professor posted his work and it is different and way simpler than mine. Would love feedback.

My work is the second page (pencil and final answer in pen).

It looks like my professor simply took the binomial expansion of just (1+B)^(3/2) using B=(1/x) and forgot to take into account the minus sign on the exponent. Forgivable, but I don't think that is the right way to tackle this.

I algebraically manipulated (1+1/x) to get (1/x)(1+x). Then wanting to pull the term (1/x) out of the entire expansion I had to take it out of the (-2/3) power making it 1/(x^-3/2) which is x^(3/2). Then I took the expansion of (1+x)^(-3/2) and mutliplied it by my factor of (x^(3/2)).

Anyone care to take a crack at this?

THANKS!

I will not read posted images, only typed work.

However, as you have described it, your expansion (if correct) would be valid only for $0 < x < 1$, while that of your professor (when corrected) would only be valid for $|x| > 1$. So, their regions of validity would be different.