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2001×2003/2002 + 2002×2004/2003 + 4005/(2002×2003)
=(2002-1)(2002+1)/2002 + (2003-1)(2003+1)/2003 + (2×2002+1)/(2002×2003)
=(2002²-1)/2002 + (2003²-1)/2003 + (2×2002+1)*[1/2002 - 1/2003)
=2002²/2002 - 1/2002 + 2003²/2003 - 1/2003 + 2 -2×2002/2003+1/2002-1/2003
=2002 - 1/2002 + 2003 - 1/2003 + 2 + 1/2002 +2-(2-2/2003)+1/2002-1/2003
=4007 - 1/2003
=(2002-1)(2002+1)/2002 + (2003-1)(2003+1)/2003 + (2×2002+1)/(2002×2003)
=(2002²-1)/2002 + (2003²-1)/2003 + (2×2002+1)*[1/2002 - 1/2003)
=2002²/2002 - 1/2002 + 2003²/2003 - 1/2003 + 2 -2×2002/2003+1/2002-1/2003
=2002 - 1/2002 + 2003 - 1/2003 + 2 + 1/2002 +2-(2-2/2003)+1/2002-1/2003
=4007 - 1/2003
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答案是4005.
追答
2001×2003/2002 + 2002×2004/2003 + 4005/(2002×2003)
=(2002-1)(2002+1)/2002 + (2003-1)(2003+1)/2003 + (2×2002+1)/(2002×2003)
=(2002²-1)/2002 + (2003²-1)/2003 + (2×2002+1)*[1/2002 - 1/2003)
=2002²/2002 - 1/2002 + 2003²/2003 - 1/2003 + 2 -2×2002/2003+1/2002-1/2003
=2002-1/2002+2003-1/2003+2-(2-2/2003)+1/2002-1/2003
=4005-1/2002-1/2003+2/2003+1/2002-1/2003
=4005
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