Cross Cross Cross

Calculus Level 2

\[\left (1+\frac { 2 }{ 3+1 } \right)\left (1+\frac { 2 }{ { 3 }^{ 2 }+1 } \right)\left (1+\frac { 2 }{ { 3 }^{ 3 }+1 } \right) \cdots = \ ? \]

This problem is part of the set AMSP.