Evaluate the alternating sum 1 − 2 + 3 − 4 + 5 − 6 + … up to 100 terms.

Introduction / Context:We sum the first 100 integers with alternating signs. Grouping consecutive pairs simplifies the computation because each pair contributes a constant amount.

Given Data / Assumptions:

• Series: 1 − 2 + 3 − 4 + … up to 100 terms (i.e., through 100).
• Standard integer arithmetic; no special series formula required.

Concept / Approach:

• Group terms in pairs: (1 − 2), (3 − 4), (5 − 6), …
• Each pair equals −1.
• There are 100/2 = 50 such pairs.

Step-by-Step Solution:

Verification / Alternative check:Partial sums oscillate: S_2 = −1, S_4 = −2, … S_100 = −50, confirming the pairwise method.

Why Other Options Are Wrong:

• −150, −60, −100: Do not reflect the consistent −1 per pair across 50 pairs.
• None of these: Not applicable; −50 is exact.

Common Pitfalls:

• Stopping at 99 terms (odd count) by mistake.
• Miscounting the number of pairs.

Final Answer:−50