Triple progress

Algebra Level 3

(1+23+(23)2+)+(1+34+(34)2+)+(1+45+(45)2+)=?\left(1+ \frac 23 + \left(\frac 23\right)^2 +\cdots \right) + \left(1 + \frac 34 + \left(\frac 34 \right)^2 + \cdots \right) + \left(1 + \frac 45 + \left(\frac 45 \right)^2 + \cdots \right) = \, ?

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