1-2²-3²+4²+5²-.-22²-23²+24²
=(4²-3²)-(2²-1²)+(8²-7²)-(6²-5²)+.+(24²-23²)-(22²-21²)
然后根据完全平方公式a²-b²=(a+b)(a-b),得
原式=(4+3)(4-3)-(2+1)(2-1)+(8+7)(8-7)-(6+5)(6-5)+.+(24+23)(24-23)-(22+21)(22-21)
=(4+3)×1-(2+1)×1+(8+7)×1-(6+5)×1+.+(24+23)×1-(22+21)×1
=4+3-2-1+8+7-6-5+.+24+23-22-21
=(4-2)+(3-1)+(8-6)+(7-5)+.+(24-22)+(23-21)
=2+2+.+2 (12个2)
=24