100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?

Since you can notice that there are fifty pairs of n^2 – (n-1) ^2,

n^2 – (n-1)^2 = n + (n – 1)

Thus 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 can also be written as

100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050