Question 1201544
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You have a geometric progression with the 1st term a = 1/2 and the common ratio r = 1/4.


The general formula for the sum of such progression is  S = {{{a/(1-r)}}},  provided |r| < 1.


Substituting a = 1/2, r = 1/4 into the formula, you get the answer to your question

    the sum = S = {{{((1/2))/((1-1/4))}}} = {{{((1/2))/((3/4))}}} = {{{4/(2*3)}}} = {{{2/3}}}.
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Solved, with all necessary explanations.