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The sum of an inifnite geometric series is 10.  The first term and ratio are equal.  What is the first term?

 May 25, 2020
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The formula for the sum of an infinite geometric series is:  Sum  =  a / (1 - r)

where a is the first term, r is the common ratio and |r| < 1.

 

If the sum is 10 and the first term and ratio are equal (call this value x):

              10  =  x / (1 - x)

     10(1 - x)  =  x                     (cross multiply)

      10 - 10x  =  x

               10  =  11x

                 x  =  10/11

 May 25, 2020

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