- #1
Ed Quanta
- 297
- 0
I have to use Cauchy's Double Series Theorem and the following equation,
1/(1-z)^2= 1 + 2z + 3z^2 + 4z^3 + 5z^4+...
to prove that
z/(1+z) - 2z^2/(1 + z^2) + 3z^3/(1+z^3)-+...=
z/(1+z)^2 - z^2/(1+z^2)^2 + z^3/(1+z^3)^2-+...
Any hints on how to start?
Note, |z|<1
(I am not sure, but I think it might be easiest to prove this true where z is real, and then use the identity theorem to show this is true where z is complex)
1/(1-z)^2= 1 + 2z + 3z^2 + 4z^3 + 5z^4+...
to prove that
z/(1+z) - 2z^2/(1 + z^2) + 3z^3/(1+z^3)-+...=
z/(1+z)^2 - z^2/(1+z^2)^2 + z^3/(1+z^3)^2-+...
Any hints on how to start?
Note, |z|<1
(I am not sure, but I think it might be easiest to prove this true where z is real, and then use the identity theorem to show this is true where z is complex)