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#
