<PRE><B>Question 1120489</B>
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&lt;pre&gt;
If I understand your writing correctly, you are asking about the sum


    {{{1/3-1/4}}} + {{{1/4-1/5}}} + {{{1/5-1/6}}} + . . . + {{{1/31-1/32}}}


Now notice that all intermediate terms cancel each other, since each pair has opposite signs.


The only survived terms are very first and very last,  {{{1/3}}} - {{{1/32}}}.


You may simplify it further, if you want or if you need . . . 
&lt;/pre&gt;

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