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Lilit [14]
4 years ago
5

I don't know how to approach it, I've been looking at my notes and I can't grasp it.

Mathematics
1 answer:
JulijaS [17]4 years ago
5 0

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.

_____

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)

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