An Interesting Radical Expression #algebra

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[anestismoutafidis]

[x+2(x-1)^1/2]^1/2 <=>
[x+(4x-4)]^1/2; Put for x variable 1:
[1+2(1-1)^1/2]^1/2 =(1+0)^1/2=1
If we make x bigger, the solution of this expression rises degressive. For this, we have to define as solution the following series expression:
Σ [1-n] with i=[1+(n)]=i(x) {[1+(1)^1/2], [1+(2)^1/2], [1+(3)^1/2], [1+(4)^1/2], ℝ+