Question

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

Answer 1

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 finite sequence:

  S = a₁((rⁿ -1)/(r -1))

When the common ratio r has a magnitude less than 1, 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)