计算:1²-2²+3²-4²+…+99²-100²

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计算:1²-2²+3²-4²+…+99²-100²

计算:1²-2²+3²-4²+…+99²-100²
计算:1²-2²+3²-4²+…+99²-100²

计算:1²-2²+3²-4²+…+99²-100²
1²-2²+3²-4²+…+99²-100²
=(1+2)(1-2)+(3+4)(3-4)+……+(99+100)(99-100)
=-(1+2+3+4+……+99+100)
=-5050

1² - 2² + 3² - 4² +…+ 99² - 100²
= (1² - 2²) + (3² - 4²) +…+ (99² - 100²)
= (1 + 2)(1 - 2) + (3 + 4)(3 - 4) + .. + (99 + 100)(990 ...

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1² - 2² + 3² - 4² +…+ 99² - 100²
= (1² - 2²) + (3² - 4²) +…+ (99² - 100²)
= (1 + 2)(1 - 2) + (3 + 4)(3 - 4) + .. + (99 + 100)(990 - 100)
= -(1 + 2 + 3 + 4 + ... + 99 + 100)
= - [(1 + 100) + (2 + 99) + ... + (50 + 51)]
= - 101×50
= - 5050

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