Question

计算1²-2²+3²-4²+…+99²-100²

计算1²-2²+3²-4²+…+99²-100²

Answer 1

n^2 - (n+1)^2 = (n+n+1)[n-(n+1)] = -n - (n+1)
所以结果为 -1 - 2 - 3 - …… - 99 - 100
=-（1+2+……+99+100）
=-5050

Answer 2

1²-2²+3²-4²+…+99²-100²
=-(2²-1²+4²-3²+……+100²-99²)
=-[(1+1)²-1²+(3+1)²-3²+……+(99+1)²-99²]
=-5050