Alternating Sum
Given that the number 2008 is the correct answer to a sum, can you find n?
Given that the number 2008 is the correct answer to the calculation below, what is $n?$$$1-2+3-4+5-6+...+(n-2)-(n-1)+n$$
Answer: 4015
Image
![Alternating Sum Alternating Sum](/sites/default/files/styles/large/public/thumbnails/content-id-5707-alternating%252520sum.png?itok=0DYGHjD_)
Add 1 for each odd number
$\therefore$ $n$ is the 2008th odd number
Which is 2008$\times$2$-$1 = 4015
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.