100X100—99X99+98X98+...+2X2—1X1等于多少

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100X100—99X99+98X98+...+2X2—1X1等于多少
100X100—99X99+98X98+...+2X2—1X1等于多少

100X100—99X99+98X98+...+2X2—1X1等于多少
=（100+99）（100-99）+（98+97）（98-97）...+（2+1）（2-1）
然后就是一个等差数列,答案为5050

S= 100X100—99X99+98X98+...+2X2—1X1
=∑(2n)²-∑(2n-1)²
=∑(4n-1)
=4n(n+1)/2 - n
=2n(n+1) - n
= 2x50x(50+1) - 50
=5050

将一正一负的两项放在一起，利用平方差公式展开，将会得到一个等差数列，再用等差数列求和公式算。

S= 100X100—99X99+98X98+...+2X2—1X1
=∑(2n)-∑(2n-1)
=∑(4n-1)
=4n(n+1)/2 - n
=2n(n+1) - n
= 2x50x(50+1) - 50
=5050

100X100—99X99+98X98+...+2X2—1X1 100X100—99X99+98X98+...+2X2—1X1等于多少 100X100一99X99+98X98一97X97+,十2X2一1X1 100X100-99X99-98X98-97X97+…+2X2-1X1=? 计算100X100-99X99+98X98-97X97+...+2X2-1X1= 1X1+2X2+3X3+4X4+5X5.+98X98+99X99+100X100=? 100x100-99x99+98x98-97x97+.+4x4-x4-3x3+2x2-1计算 0.25x0.25x...x0.25x4x...x4=1x2分之1+2x3分之1+3x4分之1+4x5分之1+...+97x98分之1+98x99分之1+99x100分之1=(1+2分之1）x（1+3分之1）x（1+4分之1）x...(1+18分之1）x（1+19分之1）x（1+20分之1）= 2x4/1+4x6/1+6x8/1.+96x98/1+98x100/1= 1/1X2+1/2x3+1/3x4+1/4x5+.+1/98x99+1/99x100求结果! 求1x2,2x3,3x4,4x5,……98x99,99x100的倒数和如题 1/1x2+1/2x3+1/3x4+……+1/98x99+1/99x100=…… 2/1x2+2/2x3+2/3x4+2/4x5+...+2/98x99+2/99x100 1x2+2x3+3x4+4x5+······98x99+99x100=? 1/1x2+1/2x3+1/3x4+.1/98x99+1/99x100=?要注明运算过程 1/1x2+1/2x3+1/3x4.1/98x99+1/99x100怎么解 1x2/1+2x3/1+3x4/1+……+98x99/1+99x100/1=? 1x1-2x2+3x3-4x4******+99x99-100x100+101x101的过程教教我