I have tried a million times, but still cannot get the right fraction. Please get the answer with the infinte geometric series method, as more than one method will only confuse me more at this point. Thanks for your time!
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hint : x = 0.2777777---> 10 x = 2 .777777---> 9 x = 2.5 ----> x = 25 / 90
0.2 + 7 / 100 + 7 / 1000 + 7 / 10000 +.....= 0.2 + 7/10 [ 1/10 + 1/100 + ...]
= 0.2 + 7/10 { 1/10 / [ 1 - 1/10] } = 0.2 +7/10 { 1 / 9} = 18 / 90 + 7 / 90 = 25 / 90
0.2 + 7 / 100 + 7 / 1000 + 7 / 10000 +.....= 0.2 + 7/10 [ 1/10 + 1/100 + ...]
= 0.2 + 7/10 { 1/10 / [ 1 - 1/10] } = 0.2 +7/10 { 1 / 9} = 18 / 90 + 7 / 90 = 25 / 90
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??