Question

Cine poate sa ma ajute si pe mine cu exercițiul 4 va rog frumosss?

Answer 1

Răspuns:

4,(1)=4,1/9=(9*4+1)/9=37/9

37/37/9=1/1/9=9

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4,(2)=4,2/9=(4*9+2)/9=38/9

38/38/9=1/1/9=9

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4,(3)=4,3/9=(4*9+3)/9=39/9

39/39/9=1/1/9=9

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4,(4)=4,4/9=(9*4+4)/9=40/9

40/40/9=1/1/9=9

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4,(8)=4,8/9=(9*4+8)/9=44/9

44/44/9=1/1/9=9

a=√9+√9+√9+...+√9(de   8   ori)=

3+3+3+....+3=3*8=24

Explicație pas cu pas:

Answer 2

$\it \forall \ n-cifr\breve a\ (n\ne 9) \Rightarrow 4,(n) =4\dfrac{n}{9}=\dfrac{36+n}{9}\\ \\ \\ Prin\ \ urmare,\ vom\ avea:\\ \\ \\ a=\sqrt{\dfrac{37}{\frac{37}{9}}}+\sqrt{\dfrac{38}{\frac{38}{9}}}+\sqrt{\dfrac{39}{\frac{39}{9}}}+\ ...\ +\sqrt{\dfrac{44}{\frac{44}{9}}}=\underbrace{\sqrt9+\sqrt9+\sqrt9+\ ...\ +\sqrt9}_{8\ termeni}=24$