(1 -⅔)• (1 -3) (1 -1)...(1 -20252)

To simplify the expression \((1 - \frac{2}{3}) \cdot (1 - 3) \cdot (1 - 1) \cdots (1 - 20252)\), we will evaluate each individual term in the product.

1. Calculate each term:

   • The first term: \(1 - \frac{2}{3} = \frac{1}{3}\)
   • The second term: \(1 - 3 = -2\)
   • The third term: \(1 - 1 = 0\)
   • For any integer \(k\) where \(k \geq 1\): \(1 - k\) will continue to produce negative integers (for example, \(1 - 2 = -1\), \(1 - 4 = -3\), etc.).
   • The last term: \(1 - 20252 = -20251\)

2. Notice that since one of the terms in the product is \(1 - 1 = 0\), the entire product will equal zero.

Thus, the value of the expression \[ (1 - \frac{2}{3}) \cdot (1 - 3) \cdot (1 - 1) \cdots (1 - 20252) = 0. \] Therefore, the answer is \[ \boxed{0}. \]