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1. Alternating sum of integers up to 2007 ●○○○○ 10 ptsFind the value of $1 - 2 + 3 - 4 + \cdots + 2005 - 2006 + 2007$.
2. Smallest non-negative signed sum ●●○○○ 20 ptsInsert $+$ or $-$ signs between the numbers $1, 2, 3, \ldots, 1989$, so that the sum is $\pm1\pm2\pm3\cdots\pm1989$ with the first number taken as $+$. What is the smallest non-negative value that the sum can take?
3. Alternating sum of a linear sequence ●●○○○ 20 ptsThe $n$th term of a sequence is $a_n = (-1)^{n+1}(3n + 2)$. What is the value of $a_1 + a_2 + \dots + a_{100}$?
4. Alternating sum in steps of four ●●○○○ 20 ptsFind the value of $2013-2009+2005-2001+\cdots+29-25$.
5. Sum of alternate terms of a sequence ●●●○○ 50 ptsA sequence consists of 2010 terms. Each term after the first is 1 larger than the previous term. The sum of the 2010 terms is 5307. When every second term is added up, starting with the first term and ending with the second last term, what is the sum?