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se considera x = 1+2+3+....+2017 si y = 2+4+6+....+2018 scrieety raportul x/y

Răspuns :

x = 1 + 2 + .. + 2017 = 2017·2018 : 2 = 2017·1009

y = 2 + 4 + .. 2018 = 2·(1 + 2 + .. + 1009) = 2·1009·1010 : 2 = 1009·1010

x/y = 2017·1009/1009/1010 = 2017/1010

Am folosit formula lui Gauss care spune cam asa ...

1 + 2 + .. + n = n·(n + 1) : 2