Question

3. Valoarea sumei 1 supra 0,0(5)+1 supra 0,0(05)+1supra 0,0(005)+0,0(0005) este:A.22212 B.22012C.{1,2,3,5} D.{0,1,2,3,4,5}

1
+
+
este:
0,0(5) 0,0(05) 0,00005) 0,000005)
A. 22212
B. 22012
C. 22232
( 3° / 3°./ 34
>​

Answer 1

Răspuns:

$\boxed{\bf S=22\,212}$

Explicație pas cu pas:

$\bf S=\dfrac{1}{0,0(5)} + \dfrac{1}{0,0(05)} + \dfrac{1}{0,0(005)} + \dfrac{1}{0,0(0005)}$

$\bf \;$

$\bf S = \dfrac{1}{\dfrac{5}{90} } + \dfrac{1}{\dfrac{5}{990} } + \dfrac{1}{\dfrac{5}{9990} } + \dfrac{1}{\dfrac{5}{99990} }$

$\bf \;$

$\bf S= 1: \dfrac{5}{90} + 1: \dfrac{5}{990} +1: \dfrac{5}{9990} +1: \dfrac{5}{99990}$

$\bf \;$

$\bf S = 1 \cdot \dfrac{90}{5} + 1 \cdot \dfrac{990}{5} + 1 \cdot \dfrac{9990}{5} + 1 \cdot \dfrac{99990}{5}$

$\bf \;$

$\bf S= \dfrac{90}{5} + \dfrac{990}{5} + \dfrac{9990}{5} + \dfrac{99990}{5}$

$\bf \;$

$\bf S = \dfrac{90+990+9990+99990 }{5 }$

$\bf \;$

$\bf S= \dfrac{111\, 060}{5} = \boxed{\bf 22\, 212}$

$\bf \;$

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