Triple progress

Algebra Level 3

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