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natural number from 1 to 2013 are written in a series. Can we get its sum zero by placing + or - sign between them? If yes then by how many + and how many -? If no why? Justify your answer with proper logic.

Note by Parv Parkhiya 3 years, 11 months ago

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No. Consider parity 2.

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Sorry, I don't get it...."consider parity 2." ???????????

+- 1 +- 2 +- 3 +- ... +- 2013 = 0

LHS mod 2 = 1, RHS mod 2 = 0, contradiction

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TopNewestNo. Consider parity 2.

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Sorry, I don't get it...."consider parity 2." ???????????

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+- 1 +- 2 +- 3 +- ... +- 2013 = 0

LHS mod 2 = 1, RHS mod 2 = 0, contradiction

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