(文)Sn=1-2+3-4+5-6+…+(-1)n+1•n,则S100+S200+S301等于( )A.1B.-1C.51D.52
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(文)Sn=1-2+3-4+5-6+…+(-1)n+1•n,则S100+S200+S301等于( ) |
答案
∵Sn=1-2+3-4+5-6+…+(-1)n+1•n, ∴S100=1-2+3-4+5-6+…+(-100)=(1-2)+(3-4)+…+(99-100)=-1×50=-50, S200=1-2+3-4+5-6+…+(-200)=(1-2)+(3-4)+…+(199-200)=-1×100=-100, S301=1-2+3-4+5-6+…+301=1+(3-2)+(5-4)+…+(301-300)=1+150=151, ∴S100+S200+S301=-50-100+151=1, 故选:A. |
举一反三
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