Respostas

2014-08-31T15:04:05-03:00
Letra d) 2.
 
 1/1 + 1/2 + 1/3 + 1/6 
 o mmc de 1,2,3 e 6 é = 6, logo:

6/6 + 3/6 + 2/6 + 1/6 = 12/6 = 2
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  • Usuário do Brainly
2014-08-31T15:05:10-03:00
Olá, Lívia !

Seja S o valor dessa soma.

S=1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}
 
Veja que, \text{mmc}(2,3,6)=6. Assim:

S=\dfrac{6\times1+3\times1+2\times1+1}{6}=\dfrac{6+3+2+1}{6}

S=\dfrac{12}{6}=2

\text{Alternativa D}.

De fato pois:

1+\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=1+\left(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\right)

Note que, \dfrac{1}{3}+\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{1}{2}.

Daí segue que, \dfrac{1}{2}+\dfrac{1}{3}=\dfrac{1}{6}=\dfrac{1}{2}+\dfrac{1}{2}=1.

Somando com o 1, obtemos 2.
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