Răspunsuri

Cel mai inteligent răspuns!
2014-10-25T11:10:48+03:00
b = 1 + 3 + 5 + .... + 2011 = 1 + 2 + 3 + 4 + .... + 2010 + 2011 - 2 - 4 - 6 - .... - 2010 = 1 + 2 + 3 + .... + 2011 - 2 ( 1 + 2 + 3 + .... + 1005 ) = 2011 × 2012 ÷ 2 - 2 × 1005 × 1006 ÷ 2 =  2011 × 1006 - 1005 × 1006 = 1006 ( 2011 - 1005 ) = 1006 × 1006 = 1006² ==> b este patrat perfect
2014-10-25T12:05:57+03:00
b = 1 + 3 + 5 + .... + 2011 = 1 + 2 + 3 + 4 + .... + 2010 + 2011 - 2 - 4 - 6 - .... - 2010 = 1 + 2 + 3 + .... + 2011 - 2 ( 1 + 2 + 3 + .... + 1005 ) = 2011 × 2012 ÷ 2 - 2 × 1005 × 1006 ÷ 2 =  2011 × 1006 - 1005 × 1006 = 1006 ( 2011 - 1005 ) = 1006 × 1006 = 1006² = Patrat perfect !
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