### Instruction: Compute $1-2+3-4+ \dots -98+99$ .### Response: This is an alternating series, where the sign changes for each term.
One way to approach this is to group the terms in pairs, starting from the left.
For example, $(1-2) + (3-4) + \dots + (97-98) + 99$.
Each pair, except the last one, has a sum of $-1$.
So, there are $49$ pairs of $-1$, and then an extra $99$ at the end.