Răspuns:
Explicație pas cu pas:
a) a = 1 + 2 + 3 + ..... + 49
a = 49 × (1+49) : 2
a = 49 × 50 : 2
a = 7² x 25
a = 7² x 5² ⇒ a = (7x5)² ⇒ a = 35² → pătrat perfect
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c)
a = 1+3+5+7+.....+2011
(2011-1) : 2 + 1 = 2010 : 2 + 1 = 1005 + 1 = 1006 termeni are suma
a= 1006 × ( 1+2011) : 2
a= 1006 × 2012 : 2
a = 1006 × 1006
a = 1006²→ pătrat perfect
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e)
a = 2 × (1+2+3+.......+24) + 25
a = 2× 24 × (1+24) : 2 + 25
a = 24×25 + 25
a = 25×(24+1)
a = 25 × 25
a = 25² → pătrat perfect
