Peace Operator

Algebra Level 4

Consider the operation \(\large ☮\) with the following properties: \[ \large a☮b=a+b+ab\\ \large a☮b☮c=(a☮b)☮c \]

Evaluate \[\large \frac { 1 }{ 2 } ☮\frac { 1 }{ 3 } ☮\frac { 1 }{ 4 } ☮ \ldots☮\frac { 1 }{ 2015 }. \]