1x3 / 2 + 3x5 / 2 + 5x7 / 2 + 7x9 / 2 + +2 / 1997x1999 + 2 / 1999x2001 It's necessary tonight! Hurry!

1x3 / 2 + 3x5 / 2 + 5x7 / 2 + 7x9 / 2 + +2 / 1997x1999 + 2 / 1999x2001 It's necessary tonight! Hurry!

2/1×3=1/1-1/3
2/3×5=1/3-1/5
……
2/1999×2001=1/1999-1/2001
Add it all up, and the positive and negative in the middle cancel out
So the original formula = 1-1 / 2001 = 2000 / 2001

Calculate 1 / 1x3 + 1 / 3x5 + 1 / 5x7 + +Value of 1 / 99x101

Can be converted to
1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+… +1/2(1/99-1/101)
=1/2(1-1/101)
=50/101

1/1X3+1/2X4+1/3X5…… +1/9X11=?,

36 / 55

How to calculate 1 / 1x3 + 1 / 3x5 +... 1 / 9x11 in a simple way?

1/1x3+1/3x5+...1/9x11=1/2×（1－1/3）+1/2×（1/3-1/5)+… 1/2×（1/9-1/11)=1/2-1/22=10/22=5/11