1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
来源:学生作业帮助网 编辑:六六作业网 时间:2025/02/03 14:48:45
1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
1x1-2x2+3x3-4x4+5x5-6x6.-100x100+101x101
=1^2-2^2+3^2-4^2+5^2-6^2.-100^2+101^2
=(1-2)(1+2)+(3-4)(3+4)+.(99-100)(99+100)+101^2
=-(1+2+3+4.+99+100)+101^2
=-101*50+101^2
=101*(101-50)
=5151
(1+2)(1-2)......(99+100)(99-100)+101*101
=-3-7-11-.....-199+10201
=-5050+10201
=5151
-k^2+(k+1)^2=2k+1 k=2,4,6,...,100
所以原式=1*1+2*(2+100)*50/2+50=5151
利用平方差公式:
1*1-2*2+3*3-4*4+5*5……-100*100+101*101
=1*1+(3*3-2*2)+(5*5-4*4)……+(101*101-100*100)
=1*1+(3+2)*(3-2)+(5+4)*(5-4)+……+(101+100)*(101-100)
=1+5*1+9*1+……+201*1
=1+5+9+……+201(共...
全部展开
利用平方差公式:
1*1-2*2+3*3-4*4+5*5……-100*100+101*101
=1*1+(3*3-2*2)+(5*5-4*4)……+(101*101-100*100)
=1*1+(3+2)*(3-2)+(5+4)*(5-4)+……+(101+100)*(101-100)
=1+5*1+9*1+……+201*1
=1+5+9+……+201(共有51项,成等差数列)
=(1+201)*51/2(等差数列求和公式)
=5151
收起