Determine the value of \(2002 + \frac{1}{2} \left( 2001 + \frac{1}{2} \left( 2000 + \dots + \frac{1}{2} \left( 3 + \frac{1}{2} \cdot 2 \right) \right) \dotsb \right).\)
The "closed form" of this sequence can be represented as:
n + 1/2(2n - 4) =2002 + 1/2(2*2002 - 4) =2002 + 2000 =4002