Question

Đã trả lời bởi chuyên gia

Answer 1

`A=1/2+1/4+1/8+1/16+1/32+1/64+1/128`

`A=64/128+32/128+16/128+8/128+4/128+2/128+1/128`

`A=(64+32+16+8+4+2+1)/128`

`A=127/128`

`-------------------------------------------------------------`

`B = 1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625`

`5B = 5 xx (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)`

`5B = 1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125`

`5B - B = (1 + 1/5 + 1/25 + 1/125 + 1/625 + 1/3125) - (1/5 + 1/25 + 1/125 + 1/625 + 1/3125 + 1/15625)`

`4B = 1 - 1/{15625}`

`4B = {15624}/{15625}`

`B = {15624}/{15625} : 4`

`B = {3906}/{15625}.`

Vậy `B = {3906}/{15625}.`

Answer 2

$A = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} \Rightarrow 2 A = 2 . (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128}) \Rightarrow 2 A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} \Rightarrow 2 A - A = (1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64}) - (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128}) \Rightarrow A = 1 - \frac{1}{128} \Rightarrow A = \frac{127}{128}$

$B = \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625} \Rightarrow 5 B = 5 . (\frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625}) \Rightarrow 5 B = 1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} \Rightarrow 5 A - A = (1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125}) - (\frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625}) \Rightarrow 4 A = 1 - \frac{1}{15625} \Rightarrow 4 A = \frac{15624}{15625} \Rightarrow A = \frac{3906}{15625}$ ...

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Answer 3

$A = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128} \Rightarrow 2 A = 2 . (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128}) \Rightarrow 2 A = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} \Rightarrow 2 A - A = (1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64}) - (\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \frac{1}{32} + \frac{1}{64} + \frac{1}{128}) \Rightarrow A = 1 - \frac{1}{128} \Rightarrow A = \frac{127}{128}$

$B = \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625} \Rightarrow 5 B = 5 . (\frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625}) \Rightarrow 5 B = 1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} \Rightarrow 5 A - A = (1 + \frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125}) - (\frac{1}{5} + \frac{1}{25} + \frac{1}{125} + \frac{1}{625} + \frac{1}{3125} + \frac{1}{15625}) \Rightarrow 4 A = 1 - \frac{1}{15625} \Rightarrow 4 A = \frac{15624}{15625} \Rightarrow A = \frac{3906}{15625}$ ...

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