Mathematics

Question

The answer is 16, I am just not sure how to arrive at that answer.
The answer is 16, I am just not sure how to arrive at that answer.

1 Answer

  • Step-by-step explanation:

    ∑ (4ⁿ⁺¹ / 5ⁿ)

    Rewrite 4ⁿ⁺¹ as 4 (4ⁿ).

    ∑ 4 (4ⁿ / 5ⁿ)

    ∑ 4 (4/5)ⁿ

    This is a geometric series.  The sum of an infinite geometric series is:

    S = a / (1 −r)

    where a is the first term and r is the common ratio.

    Here, the first term is 16/5 (because n starts at 1), and the common ratio is 4/5.

    S = 16/5 / (1−4/5)

    S = 16/5 / (1/5)

    S = 16

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