What us the easiest way to find the solution to 1+2-3+4+5-6+7+8-9+...+208+209-210 ?

What us the easiest way to find the solution to 1+2-3+4+5-6+7+8-9+...+208+209-210 ?

Hello Guest!

The easiest way to do this is with the Gaussian empirical formula.

$\sum\limits_{k=1}^{n} k =\dfrac{n(n+1)}{2}$

$\sum\limits_{k=1}^{209} k-210 ={\color{black}\dfrac{209(209+1)}{2}-210=}21735$

  !

Find  sum of arithmetic sequence:    Sum =    209/2 ( 1 + 209)           then subtract   210   to get    21 735