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Answer to Question #22150 in Algebra for jyothsna
Question #22150
1+2-3+4+5-6+7+8-9+.....................................+2002+2003-2004+2005+2006-2007. what is the value of this expression
Expert's answer
1+2-3+4+5-6+7+8-9+10+11-12+13+14-15+...+2005+2006-2007=
=3-3+9-6+15-9+21-12+27-15+...+2004=3+6+9+12+...+2004=
=3*1+3*2+3*3+3*4+...+3*668=3*(1+2+3+4+...+668)=3*(668*(668+1)/2)=3*223446=670338.
=3-3+9-6+15-9+21-12+27-15+...+2004=3+6+9+12+...+2004=
=3*1+3*2+3*3+3*4+...+3*668=3*(1+2+3+4+...+668)=3*(668*(668+1)/2)=3*223446=670338.
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