Sum it up

Algebra Level 2

If the first three terms of a geometric progression are given to be 2+1,1,21, \sqrt2+1,1,\sqrt2-1, find the sum to infinity of all of its terms.

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

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