2/1x2+2/2x3+2/3x4+2/4x5+...+2/98x99+2/99x100

2/1x2+2/2x3+2/3x4+2/4x5+...+2/98x99+2/99x100
=2（1/1x2+1/2x3+1/3x4+1/4x5+...+1/98x99+1/99x100）
=2*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+............+1/98-1/99+1/99-1/100)
=2*(1-1/100)
=2*99/100
=99/50

2/1x2+2/2x3+2/3x4+2/4x5+...+2/98x99+2/99x100
=2×（1-1/2+1/2-1/3+……+1/99-1/100）
=2×（1-1/100）
=2×99/100
=99/50