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
③
×9 15
+14 17
×8 17
14 15
④1×2+2×3+3×4+4×5+…+18×19+19×20.
答
①2008×2010×(
+1 2008×2009
)1 2009×2010
=2008×2010×
+2008×2010×1 2008×2009
,1 2009×2010
=
+2010 2009
,2008 2009
=
,4018 2009
=2.
②2000×20102010-2010×20002000
=2000×2010×10001-2010×2000×10001,
=0;
③
×9 15
+14 17
×8 17
14 15
=
×9 15
+14 17
×14(1 17
×8),1 15
=
×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.