Evaluate 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 =?
Options
A) 3043
B) 5050
C) 5176
D) 9356
E) 4890
B   5050   You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.   n^2 – (n-1)^2 = n + (n – 1)   In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
<result>B</result>
Evaluate 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 =?