Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.

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Solution

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50
= (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + ... + (49 − 50)
= (− 1) + (− 1) + (− 1) + ... + 25 terms
= (− 1) $×$ 25
= − 25
Hence, 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50 = − 25.

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Calculate 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50.

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50 = (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + ... + (49 − 50) = (− 1) + (− 1) + (− 1) + ... + 25 terms = (− 1) × 25 = − 25 Hence, 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50 = − 25.

1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50
= (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + ... + (49 − 50)
= (− 1) + (− 1) + (− 1) + ... + 25 terms
= (− 1) $×$ 25
= − 25
Hence, 1 − 2 + 3 − 4 + 5 − 6 + 7 − 8 + ... + 49 − 50 = − 25.