Question 1186693
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Find the sum of the series 15/42+15/56+15/72+15/90+…+15/9900
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The series is 15 times  S = {{{1/42 + 1/56 + 1/72 + 1/90 + ellipsis + 1/9900}}}


Each addend in the sum S is


    {{{1/42}}} = {{{1/6 - 1/7}}}         (1)

    {{{1/56}}} = {{{1/7 - 1/8}}}       
    
    {{{1/72}}} = {{{1/8 - 1/9}}}

    {{{1/90}}} = {{{1/9 - 1/10}}}

       . . . and so on . . . 

    {{{1/9900}}} = {{{1/99 - 1/100}}}     (last)


The pattern is clear.


When you add the lines from (1) to the (last),  all  intermediate terms with opposite signs will cancel each other, 

leaving only  {{{1/6 - 1/100}}} = {{{(100-6)/600}}} = {{{94/600}}}.


So the <U>ANSWER</U> to the problem's question is  {{{15*(94/600)}}} = {{{94/40}}} = {{{47/20}}} = 2.35.
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Solved, answered and explained.