Question

a) (1-2+3-4+5-6+ ... +2009-2010) ∙2+2010
b) -5-10-15- ... -2005-2010+(1+2+3+ ... 402)
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Answer 1

Răspuns:

a) (1-2 + 3-4 + 5-6 + ... + 2009-2010)×2 + 2010 =

= (-1 + -1 + -1 + ...+ -1)×2 + 2010

= (-1 × 1005)×2 + 2010

= - 1005×2 + 2010

= - 2010 + 2010

= 0

b) -5 - 10 - 15 - ...  - 2005 - 2010 + (1 + 2 + 3 +  .. + 402) =

= - 5(1 + 2 + 3 + .. + 402) + (1 + 2 + 3 + .. + 402)

= (1 + 2 + 3 + .. + 402)( - 5 + 1)

= (402×403/2)(-4)

= 81003(-4)

= - 324012