When does $1-2+3-4+5-\cdots +(-1)^{n+1}n$ reach $100$?

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The smallest possible integer \(n\) such that \[1-2+3-4+5-6+\cdots +(-1)^{n+1}n \geq 100\] is

1. \(99\),

2. \(101\),

3. \(199\),

4. \(300\).

What is the sum of the terms of the sequence when \(n=1\)?

What about when \(n=2\)? \(n=3\)? \(n=4\)?

When will this sum reach \(100\)?

Or… what is the sum of the first \(2n\) terms of the sequence?