Question

( UFC-CE) O valor da soma 1+1/2 + 1/3 + 1/6 é 
a ) 5 b) 4 c)3 d) 2 e ) 1 

Answer 1

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

Answer 2

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 $2$.