Alternating Sum
Given that the number 2008 is the correct answer to a sum, can you find n?
Age
14 to 16
Challenge level
Problem
Given that the number 2008 is the correct answer to the calculation below, what is $n?$$$1-2+3-4+5-6+...+(n-2)-(n-1)+n$$
Student Solutions
Answer: 4015
Image
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.