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Hi! I'm taking a course on Perturbation theory and as it's quite advanced the lecturer assumes everyone has a good level of maths. One of the parts is expanding roots of a quadratic equation about 0, I can understand how simple ones of the form $(1 + x)^2$ but I don't know where the answers are coming from for a couple I have here. This is the positive root of an equation:

$\frac{1}{2x}(1 + \sqrt{1 + 4x})$

The expansion for this is :

$1 + x + 2x^2 + 5x^3 + ...$

If anyone could explain this do me or do out the method for doing expansions of this type I would be forever grateful!!!

$\frac{1}{2x}(1 + \sqrt{1 + 4x})$

The expansion for this is :

$1 + x + 2x^2 + 5x^3 + ...$

If anyone could explain this do me or do out the method for doing expansions of this type I would be forever grateful!!!

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