# 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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