To find the value of the expression, we can simplify each term first:

1/2 * 3 = 3/2
1/3 * 4 = 4/3
1/4 * 5 = 5/4
...

Now, we can rewrite the expression as:

3/2 + 4/3 + 5/4 + ... + 2009/2008

To add these fractions, we need to find a common denominator. The common denominator for these fractions is the product of all the denominators:

2 * 3 * 4 * ... * 2008 = 2008!

Now, we can rewrite each fraction with the common denominator:

(3/2) * (2008!/2) + (4/3) * (2008!/3) + (5/4) * (2008!/4) + ... + (2009/2008) * (2008!/2008)

Simplifying each term:

3 * 2008!/2 + 4 * 2008!/3 + 5 * 2008!/4 + ... + 2009 * 2008!/2008

Now, we can add all these terms together:

(3 * 2008!/2 + 4 * 2008!/3 + 5 * 2008!/4 + ... + 2009 * 2008!/2008) = 2008! * (3/2 + 4/3 + 5/4 + ... + 2009/2008)

Therefore, the value of the expression is 2008! * (3/2 + 4/3 + 5/4 + ... + 2009/2008).