<PRE><B>Question 1191493</B>
&lt;br&gt;
Plugging in n=1, 2, 3... shows the first few terms to be&lt;br&gt;
1/10, 7/100, 49/1000, ...&lt;br&gt;
This is an infinite geometric sequence with first term 1/10 and common ratio 7/10.&lt;br&gt;
The sum of an infinite geometric sequence with first term a and common ratio r is&lt;br&gt;
{{{a/(1-r)}}}&lt;br&gt;
For this example, the sum is&lt;br&gt;
{{{(1/10)/(1-7/10) = (1/10)/(3/10) = 1/3}}}&lt;br&gt;
ANSWER: 1/3&lt;br&gt;
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