Question #2eafa

1 Answer
Jan 22, 2018

S=-2,037,171

Explanation:

We can solve this using the difference of two squares.

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

Using this fact we can write:

S=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+...+(2017-2018)(2017+2018)

=-1(1+2)-1(3+4)-1(5+6)-...-1(2017+2018)

Take out a factor of -1

S=-1(1+2+3+4+...+2017+2018)

This is -1 lots of the sum of the first 2018 integers.

S=-sum_"r=1"^2018"r

From standard results (sum_"r=1"^n"r=1/2n(n+1))

S=-2018/2xx(2018+1)

S=-2,037,171