Question 1189201
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The sum of the infinite geometric progression  P(0) + P(1) + P(2) + . . .  must be equal to 1.  It gives an equation to find "a".


The sum is equal to  {{{a/(1-2/5)}}} = {{{a/((3/5))}}} = {{{(5a)/3}}}.


So,  {{{(5a)/3}}} must be equal to 1


    {{{(5a)/3}}} = 1,


which gives  a = {{{3/5}}} = 0.6.    <U>ANSWER</U>
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Solved and explained.