Simple calculation of 2002 / 1 × 3 + 2002 / 3 × 5 + 2002 / 5 × 7 + 2002 / 7 × 9 + 2002 / 9 × 11

Simple calculation of 2002 / 1 × 3 + 2002 / 3 × 5 + 2002 / 5 × 7 + 2002 / 7 × 9 + 2002 / 9 × 11

1/1×3=(1-1/3)/2
1/3×5=(1/3-1/5)/2
1/5×7=(1/5-1/7)/2
.
.
1/9×11=(1/9-1/11)/2
2002/1×3+2002/3×5+2002/5×7+2002/7×9+2002/9×11
=2002×1/2×(1/1×3+1/3×5+1/5×7+1/7×9+1/9×11)
=2002×1/2×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=2002×1/2×(1-1/11)
=2002×1/2×10/11
=910

1—2—3+4+5—6—7+8+9—10—11… +2001-2002-2003 simple calculation process
1—2—3+4+5—6—7+8+9—10—11… +From 2001 to 2002 to 2003, the calculation process is simple and fast

1—2—3+4+5—6—7+8+9—10—11… +2001—2002—2003
=1+(—2—3+4+5)+(—6—7+8+9)+(—10—11… +(-1998-1999+2000+2001)—2002—2003
=1 + 4 + 4 +... + 4 (500 pieces in total) - 4005
=2001-4005
=-2004.

25 minus 40 divided by 16 multiplied by 2,5

6.25-40/16*2.5
=6.25-40*1/16*5/2
=6.25-25/4
=6.25-6.25
=0