How much is bracket minus 1 by 2 / 1 plus bracket minus 1 / 2 by 3 / 1 plus bracket minus 1 / 3 by 4 / 1 plus ellipsis plus minus 1 / 2012 by 1 / 2013

How much is bracket minus 1 by 2 / 1 plus bracket minus 1 / 2 by 3 / 1 plus bracket minus 1 / 3 by 4 / 1 plus ellipsis plus minus 1 / 2012 by 1 / 2013

simple form
=-（1x1/2+1/2x1/3+1/3x1/4+…… +1/2012x1/2013)
=-（1-1/2+1/2-1/3+1/3-1/4+…… +1/2012-1/2013)
=-（1-1/2013)
=-（2012/2013)
=-2012 / 2013 & nbsp; (- 2012 / 2013)

1/1x3+1/2x4+1/3x5+...+1/9X11=?

Because 1 / N (n + 2) = [1 / n-1 / (n + 2)] / 2
So 1 / 1 * 3 + 1 / 2 * 4 + 1 / 3 * 5 +... + 1 / 9 * 11
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/9-1/11)]/2
=(1+1/2-1/10-1/11)/2
=36/55

1/1X3+1/2X4+1/3X5+.+1/18X20=?

1/1X3=1/2(1/1-1/3)
1/2*4=1/2(1/2-1/4)
.
1/1X3+1/2X4+1/3X5+.+1/18X20
=1/2(1/1-1/3+1/2-1/4+1/3-1/5+.+1/18-1/20)
=1/2(1/1+1/2-1/19-1/20)
=531/760

1/1x3+1/2x4+1/3x5+

Because 1 / N (n + 2) = [1 / n-1 / (n + 2)] / 2
So 1 / 1 * 3 + 1 / 2 * 4 + 1 / 3 * 5 +... + 1 / 9 * 11
=[(1-1/3)+(1/2-1/4)+(1/3-1/5)+...+(1/9-1/11)]/2
=(1+1/2-1/10-1/11)/2
=36/55
Hope to solve your problem