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M= 1997+2×(1+2+3+...+1996) este patrat perfect?


Răspuns :

1 + 2 + 3 + ... + n = n(n + 1)/2
In cazul nostru n = 1996
M = 1997 + 2 x 1996 x 1997/2 = 1997 + 1996 x 1997 = 1997 x (1 + 1996) = 1997 x 1997 = 1997² deci patrat perfect

1997+2(1996x1997)/2=

1997(1+1996)=

1997x1997=

1997²