Power Series For a Differential Equation

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$$ y'+\left(1+\frac{2}{x}\right)y=0 $$

I have been trying to solve it all night, but everytime I try to determine the values of the constants, everything equals to zero, I'm honestly at a loss here.

Everytime i tried this is what I'm getting to.

$$ 2C_0x^{-1}+\sum _{n=0}^{\infty }\left[\left(n+1\right)C_{n+1}+C_n+2C_{n+1}\right]=0 $$

Thanks in advance for all the feedback.