Sum of area of infinite circles inside positive x axis, y axis and function $y=x^2 + 2$. Does area converge? All circles tangent to eachother.

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If i have the function $y=x^2 + 2,$ what will the area of an infinite amount of circles under the function be if the biggest circle is tangent to the y - axis, x - axis, the function and to the smaller circle next to it. And all the other circles are tangent to each other and to the positive x - axis and to the function given. Does the area converge, and if it does, what will the area be in exact form?