Precession of the perihelion - Schwarzschild metric

[tel]

Hi everyone!
I was trying to solve this question following the Hartle's book (Gravity: an introduction to Einstein’s general relativity) , exercise 9.15, but I don't know how to do the expansion of (1-2GM/c^2r) in powers of 1/c^2...

I know this sounds easy, but I couldn't get the expression from item (b)

Can someone please help me to expand to get the right answer

 

[tel]

For those who don't have the book, what I want is to get this equation:

from this one:

My problem is how to get the first term (in front of the first integral), only by expanding the (1-2GM/rc^2) in powers of 1/c^2. Someone?

 

[pervect]

What you need to do is to get the expression in the form

(1+u)^n

where u << 1

This can be expanded by the binomial theorem as

1 + n u + n(n-1) u^2 + ...

It looks like you will have to do this twice. The first step would be to consider the case where n=-1 and u = 2GM/c^2 r. Then you have to apply the same idea again with n=-1/2 and a much more complicated expression for u.

 

[tel]

Thank you!