2002²-2001²+2000²-1999²+1998²-1997²+.+2²-1²是多少?
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2002²-2001²+2000²-1999²+1998²-1997²+.+2²-1²是多少?
2002²-2001²+2000²-1999²+1998²-1997²+.+2²-1²是多少?
2002²-2001²+2000²-1999²+1998²-1997²+.+2²-1²是多少?
n^2-(n-1)^2=2n-1
所以,
2002²-2001²+2000²-1999²+1998²-1997²+.+2²-1²
=(2*2002-1)+(2*2000-1)+.+(2*2-1)
=2*(2002+2000+1998+.+4+2)-2002
=2*2(1001+1000+999+.+2+1)-2002
=2*(1001+1)*1001-1001*2
=2*(1001+1-1)*1001
=2*1001*1001
=2004002