Exercitiul este in poza. Nu pot sa ii dau de cap. Ma ajută cineva plzzz!!!

Răspuns:

x=2017/2018

Explicație pas cu pas:

1-1/2= 1/2

1-1/3=2/3

1-1/4=3/4

...............

1-1/2017=2016/2017.

cand inmultesti obtii la numărător 1*2*3*...*2016 iar la numitor 2*3*4*...*2017. simplificand ramane 1/2017

deci x* 1/2017=1/2018

asadar x=2017/2018

[tex]\it x\cdot(1-\dfrac{1}{2})\cdot(1-\dfrac{1}{3})\cdot(1-\dfrac{1}{4})\cdot\ ...\ \cdot(1-\dfrac{1}{2016})\cdot(1-\dfrac{1}{2017})=\dfrac{1}{2018} \Rightarrow\\ \\ \\ \Rightarrow\ x\cdot\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\ ...\ \cdot\dfrac{2015}{2016}\cdot\dfrac{2016}{2017}=\dfrac{1}{2018} \Rightarrow\ x\cdot\dfrac{1}{2017}=\dfrac{1}{2018}|_{\cdot2017}\Rightarrow\\ \\ \\ \Rightrarrow\ x=\dfrac{2017}{2018}[/tex]