To simplify the expression, we can rewrite it as:

(1/2)^2 + (1/5)^2 + (1/4)^2 + ... + (1/99)^2 + (1/100)^2

Now, let's calculate each term:

(1/2)^2 = 1/4
(1/5)^2 = 1/25
(1/4)^2 = 1/16
...
(1/99)^2 = 1/9801
(1/100)^2 = 1/10000

Now, let's add up all the terms:

1/4 + 1/25 + 1/16 + ... + 1/9801 + 1/10000

To find a common denominator, we can multiply each term by the product of all the denominators:

(1/4)*(25*16*...*9801*10000) + (1/25)*(4*16*...*9801*10000) + (1/16)*(4*25*...*9801*10000) + ... + (1/9801)*(4*25*16*...*10000) + (1/10000)*(4*25*16*...*9801)

Simplifying this expression is quite complex, but we can approximate the sum using numerical methods or a calculator.