What is the value of 1^2-2^2+3^2-4^2+...+99^2-100^2

1² - 2²  =  1 - 4  =  -3

3² - 4²  =  9 - 16  =  -7

5² - 6²  =  25 - 36  =  -11

7² - 8²  =  49 - 64  =  -15

This is an arithmetic series with a common diference of -4.

The last term:    (this is the 50th term)

99² - 100²  =  9801 - 10000  =  -199  

The formula for the sum of an arithmetic series is:  Sum  = n(f + l) / 2

where         n  =  number of terms (50)         f = first term (-3)          l = last term (-199)

Sum  =  (50)(-3 + -199) / 2  =  -5050