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Electric field/binomial expansion?

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Show that, for points that are far from a hoop of charge q and radius r, the electric field looks like a point charge.
Show this using a diagram and use binomial expansion.

I'm not sure if I am setting this up correctly, and I really need help on the binomial expansion. Thank you.

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The expert uses binomial expansion to examine electric fields.

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Let us consider a charged hoop of radius r with charge q uniformly distributed over it. Charge per unit length of the hoop = σ = Total charge/Circumference = q/2Πr ...(1)

Let us consider a segment of length dl of the hoop as shown in the fig..
Charge on the segment = dq = σdl ...(2)

Electric field intensity at point P on the hoop's axis (distant x from the centre of the hoop and distant s from the segment dl) = dE = (1/4Πε0) dq/s2

Substituting for dq from (2) we get: dE = (1/4Πε0) σdl/s2 ...(3)

Vector dE can be resolved into ...

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