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口算:(1)1+2+4+8+16+32+64+128+256+512=(2)1000001×999999=(3)(1+2+3+…+2007+2008+2007+…+3+2+1)÷2008=(4)(2005+2003+…+3+1)-(2+4+6+…+2002+2004)=

题目详情
口算:
(1)1+2+4+8+16+32+64+128+256+512=
(2)1000001×999999=
(3)(1+2+3+…+2007+2008+2007+…+3+2+1)÷2008=
(4)(2005+2003+…+3+1)-(2+4+6+…+2002+2004)=




▼优质解答
答案和解析
(1)1+2+4+8+16+32+64+128+256+512,
=(1+2+4+8+16+32+64+128+256+512)+1-1,
=(2+2+4+8+16+32+64+128+256+512)-1,
=(4+4+8+16+32+64+128+256+512)-1,
=(8+8+16+32+64+128+256+512)-1,
=(16+16+32+64+128+256+512)-1,
=(32+32+64+128+256+512)-1,
=(64+64+128+256+512)-1,
=(128+128+256+512)-1,
=(256+256+512)-1,
=(512+512)-1,
=1023;
(2)1000001×999999,
=(1000000+1)×999999,
=1000000×999999+1×999999,
=999999000000+999999;
=999999999999;
(3)(1+2+3+…+2007+2008+2007+…+3+2+1)÷2008,
=[(1+2007)×2007÷2×2+2008]÷2008,
=[2008×2007+2008]÷2008,
=2008×(2007+1)÷2008,
=2008×2008÷2008,
=2008;
(4)(2005+2003+…+3+1)-(2+4+6+…+2002+2004),
=2005+2003+…+3+1-2-4-6-…-2002-2004,
=(2005-2004)+(2003-2002)+…+(7-6)+(5-4)+(3-2)+1,
=1+1+…+1+1+1+1,
=1003.