Question

What is `(x+1)+(x-2)+(x+3)+(x-4)+...+(x+99)+(x-100)` ?

Answer 1

`(x+1)+(x-2)+(x+3)+(x-4)+...+(x+99)+(x-100) = 100x-50`

Explanation:

Since the signs alternate, it simplifies the problem if we group the expressions in pairs like this...

`(x+1)+(x-2)+(x+3)+(x-4)+...+(x+99)+(x-100)`

`= ((x+1)+(x-2))+((x+3)+(x-4))+...+((x+99)+(x-100))`

`= overbrace((2x-1)+(2x-1)+...+(2x-1))^"50 times"`

`= 50(2x-1)`

`= 100x-50`