Answer:
8
Step-by-step explanation:
You can skip directly to the formula for the sum of an infinite sequence with first term a₁ and common ratio r:
S = a₁/(1-r)
Your values of the variables in this formula are a₁ = 6 and r = 2/8. Putting these into the formula gives ...
S = 6/(1 -2/8) = 6/(6/8) = 8
The sum of the infinite geometric sequence is 8.
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The above formula is the degenerate form of the formula for the sum of a <em>finite</em> sequence:
S = a₁((rⁿ -1)/(r -1))
<em>When the common ratio r has a magnitude less than 1</em>, the term rⁿ tends to zero as n gets very large. When that term is zero, the sum of the infinite sequence is ...
S = a₁(-1/(r-1)) = a₁/(1-r)
