<PRE><B>Question 1176165</B>
&lt;br&gt;
A geometric series will converge whenever the common ratio is between -1 and 1.&lt;br&gt;
{{{-1 &lt; -3x+5/2 &lt; 1}}}&lt;br&gt;
{{{-1-5/2 &lt; -3x &lt; 1-5/2}}}&lt;br&gt;
{{{-7/2 &lt; -3x &lt; -3/2}}}&lt;br&gt;
{{{7/6 &gt; x &gt; 1/2}}}  (switch the direction of the inequality when dividing by a negative)&lt;br&gt;
{{{1/2 &lt; x &lt; 7/6}}}&lt;br&gt;
ANSWER: The series will converge for any values of x between 1/2 and 7/6.&lt;br&gt;

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