①2008×2010×(1/2008×2009+1/2009×2010) ②2000×20102010-2010×20002000 ③9/15×14/17+8/17×14/15 ④1×2+2×3+3×4+4×5+…+18×19+19×20.

问题描述:

①2008×2010×(

1
2008×2009
+
1
2009×2010

②2000×20102010-2010×20002000
9
15
×
14
17
+
8
17
×
14
15

④1×2+2×3+3×4+4×5+…+18×19+19×20.

①2008×2010×(

1
2008×2009
+
1
2009×2010

=2008×2010×
1
2008×2009
+2008×2010×
1
2009×2010

=
2010
2009
+
2008
2009

=
4018
2009

=2.
②2000×20102010-2010×20002000
=2000×2010×10001-2010×2000×10001,
=0;
9
15
×
14
17
+
8
17
×
14
15

=
9
15
×
14
17
+
1
17
×14(
1
15
×8),
=
9
15
×
4
17
+
14
17
×
8
15

=(
9
15
+
8
15
)×
14
17

=
17
15
×
14
17

=
14
15

④1×2+2×3+3×4+4×5+…+18×19+19×20
=12+1+22+2+32+3+…+192+19
=12+22+32+…+192+1+2+…+19,
=19×(19+1)×(19×2+1)÷6+(19+1)×19÷2,
=19×20×39÷6+20×19÷2,
=2470+190,
=2660.