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Ответ дал:
0
a)
представим 0,(3) как:
0,(3)=0,333...=0,3+0,03+0,003+.... - бесконечно убывающая геометрическая прогрессия со знаменателем q=0,03/0,3=0,1
формула суммы:
![S= frac{b_1}{1-q} S= frac{b_1}{1-q}](https://tex.z-dn.net/?f=S%3D+frac%7Bb_1%7D%7B1-q%7D+)
![b_1=0,3
\q=0,1
\S= frac{0,3}{1-0,1} = frac{0,3}{0,9} = frac{3}{9} = frac{1}{3} b_1=0,3
\q=0,1
\S= frac{0,3}{1-0,1} = frac{0,3}{0,9} = frac{3}{9} = frac{1}{3}](https://tex.z-dn.net/?f=b_1%3D0%2C3%0A%5Cq%3D0%2C1%0A%5CS%3D+frac%7B0%2C3%7D%7B1-0%2C1%7D+%3D+frac%7B0%2C3%7D%7B0%2C9%7D+%3D+frac%7B3%7D%7B9%7D+%3D+frac%7B1%7D%7B3%7D+)
остальное делается аналогично
б)
![0,(6)=0,6+0,06+0,006+...
\q= frac{0,06}{0,6} =0,1
\b_1=0,6
\S= frac{0,6}{1-0,1} = frac{0,6}{0,9}= frac{6}{9} = frac{2}{3} 0,(6)=0,6+0,06+0,006+...
\q= frac{0,06}{0,6} =0,1
\b_1=0,6
\S= frac{0,6}{1-0,1} = frac{0,6}{0,9}= frac{6}{9} = frac{2}{3}](https://tex.z-dn.net/?f=0%2C%286%29%3D0%2C6%2B0%2C06%2B0%2C006%2B...%0A%5Cq%3D+frac%7B0%2C06%7D%7B0%2C6%7D+%3D0%2C1%0A%5Cb_1%3D0%2C6%0A%5CS%3D+frac%7B0%2C6%7D%7B1-0%2C1%7D+%3D+frac%7B0%2C6%7D%7B0%2C9%7D%3D+frac%7B6%7D%7B9%7D+%3D+frac%7B2%7D%7B3%7D++)
в)
![0,(12)=0,12+0,0012+0,000012+...
\q= frac{0,0012}{0,12} =0,01
\b_1=0,12
\S= frac{0,12}{1-0,01} = frac{0,12}{0,99} = frac{12}{99} = frac{4}{33} 0,(12)=0,12+0,0012+0,000012+...
\q= frac{0,0012}{0,12} =0,01
\b_1=0,12
\S= frac{0,12}{1-0,01} = frac{0,12}{0,99} = frac{12}{99} = frac{4}{33}](https://tex.z-dn.net/?f=0%2C%2812%29%3D0%2C12%2B0%2C0012%2B0%2C000012%2B...%0A%5Cq%3D+frac%7B0%2C0012%7D%7B0%2C12%7D+%3D0%2C01%0A%5Cb_1%3D0%2C12%0A%5CS%3D+frac%7B0%2C12%7D%7B1-0%2C01%7D+%3D+frac%7B0%2C12%7D%7B0%2C99%7D+%3D+frac%7B12%7D%7B99%7D+%3D+frac%7B4%7D%7B33%7D+)
г)
![0,(28)=0,28+0,0028+0,000028+...
\b_1=0,28
\q= frac{0,028}{0,28} =0,01
\S= frac{0,28}{0,99} = frac{28}{99} 0,(28)=0,28+0,0028+0,000028+...
\b_1=0,28
\q= frac{0,028}{0,28} =0,01
\S= frac{0,28}{0,99} = frac{28}{99}](https://tex.z-dn.net/?f=0%2C%2828%29%3D0%2C28%2B0%2C0028%2B0%2C000028%2B...%0A%5Cb_1%3D0%2C28%0A%5Cq%3D+frac%7B0%2C028%7D%7B0%2C28%7D+%3D0%2C01%0A%5CS%3D+frac%7B0%2C28%7D%7B0%2C99%7D+%3D+frac%7B28%7D%7B99%7D+)
д)
![0,(19)=0,19+0,0019+0,000019+...
\b_1=0,19
\q= frac{0,0019}{0,19} =0,01
\S= frac{0,19}{1-0,01} = frac{19}{99} 0,(19)=0,19+0,0019+0,000019+...
\b_1=0,19
\q= frac{0,0019}{0,19} =0,01
\S= frac{0,19}{1-0,01} = frac{19}{99}](https://tex.z-dn.net/?f=0%2C%2819%29%3D0%2C19%2B0%2C0019%2B0%2C000019%2B...%0A%5Cb_1%3D0%2C19%0A%5Cq%3D+frac%7B0%2C0019%7D%7B0%2C19%7D+%3D0%2C01%0A%5CS%3D+frac%7B0%2C19%7D%7B1-0%2C01%7D+%3D+frac%7B19%7D%7B99%7D+)
е)
![0,(21)=0,21+0,0021+0,000021+...
\b_1=0,21
\q= frac{0,0021}{0,21} =0,01
\S= frac{0,21}{0,99} = frac{21}{99} = frac{7}{33} 0,(21)=0,21+0,0021+0,000021+...
\b_1=0,21
\q= frac{0,0021}{0,21} =0,01
\S= frac{0,21}{0,99} = frac{21}{99} = frac{7}{33}](https://tex.z-dn.net/?f=0%2C%2821%29%3D0%2C21%2B0%2C0021%2B0%2C000021%2B...%0A%5Cb_1%3D0%2C21%0A%5Cq%3D+frac%7B0%2C0021%7D%7B0%2C21%7D+%3D0%2C01%0A%5CS%3D+frac%7B0%2C21%7D%7B0%2C99%7D+%3D+frac%7B21%7D%7B99%7D+%3D+frac%7B7%7D%7B33%7D+)
представим 0,(3) как:
0,(3)=0,333...=0,3+0,03+0,003+.... - бесконечно убывающая геометрическая прогрессия со знаменателем q=0,03/0,3=0,1
формула суммы:
остальное делается аналогично
б)
в)
г)
д)
е)
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