To simplify this expression, we can first notice that each term in the parentheses is of the form (1 - 1/n^2), where n ranges from 2 to 100.

We can rewrite the expression as:

E = (1 - 1/2^2) . (1 - 1/3^2) . (1 - 1/4^2) ..... (1 - 1/100^2)

Now, we can use the formula for the difference of squares:

a^2 - b^2 = (a + b)(a - b)

Applying this formula to each term, we get:

E = (1 + 1/2) . (1 - 1/2) . (1 + 1/3) . (1 - 1/3) . (1 + 1/4) . (1 - 1/4) ..... (1 + 1/100) . (1 - 1/100)

Notice that each pair of terms cancels out, leaving us with:

E = 1 + 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 + ..... + 1/100 - 1/100

Simplifying this expression, we get:

E = 1

Therefore, the value of E is 1.