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

##### 1 Answer

Mar 11, 2017

#### 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#