Question 422414
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Hi
Geometric sequence {4,2,1,1/2,1/4...}
what is the relationship between one term to the next?? r = 1/2
a1 = 4
  {{{sum( a[n], n=1, 10 ) = a[1]((1-r^10)/(1-r))}}} 
{{{S[10]}}} = 4*(1-.5^10)/.5 = 8*.999 = 7.992 

Note: with r <|1|  Sum = a1/(1-r) = 4/.5 = 8 approximates the sum!
The sum of an infinite number of terms of this sequence = 8
(1/2)^20 = .00000095 for example,
 demonstrates what happens to value of (1-r^20) as n gets large