Sum it up

Algebra Level 2

If the first three terms of a geometric progression are given to be \( \sqrt2+1,1,\sqrt2-1, \) find the sum to infinity of all of its terms.

If the answer is in the form of \( \frac{a+b\sqrt c}d \) for positive integers \(a,b,c,\) and \(d\) with \(c\) square-free, find the minimum value of \(a+b+c+d\).

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