题目
1/2009+2/2009-3/2009-4/2009+5/2009+6/2009-7/2009-8/2009+9/2009+10/2009-...-1999/2009-2000/2009+2001
/2009+2002/2009
/2009+2002/2009
提问时间:2021-01-13
答案
1/2009+2/2009-3/2009-4/2009+5/2009+6/2009-7/2009-8/2009+9/2009+10/2009-...-1999/2009-2000/2009+2001/2009+2002/2009
=1/2009+(2/2009-3/2009)-(4/2009-5/2009)+(6/2009-7/2009)-(8/2009-9/2009)+10/2009-...-1999/2009-(2000/2009-2001/2009)+2002/2009
=1/2009-1/2009+1/2009-1/2009+1/2009-1/2009……+1/2009-1/2009+2002/2009
=2002/2009
=1/2009+(2/2009-3/2009)-(4/2009-5/2009)+(6/2009-7/2009)-(8/2009-9/2009)+10/2009-...-1999/2009-(2000/2009-2001/2009)+2002/2009
=1/2009-1/2009+1/2009-1/2009+1/2009-1/2009……+1/2009-1/2009+2002/2009
=2002/2009
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