Question 1190304
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The expression is an infinite geometric series with first term a=1 and common ratio r=2x.  The sum of an infinite geometric progression is given by the formula<br>
{{{S=a/(1-r)}}}<br>
We are told the sum is 1 1/4 = 5/4:<br>
{{{1/(1-2x)=5/4}}}<br>
take reciprocals....<br>
{{{1-2x=4/5}}}
{{{2x=1-4/5=1/5}}}
{{{x=1/10}}}<br>
ANSWER: x=1/10<br>