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Find the sum, if it exists, of the infinite geometric series related to the infinite geometric sequence described by An= 18(2)^n-1​

2 Answers

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Final answer:

The sum of the infinite geometric series related to the sequence An = 18(2)^(n-1) does not exist, as the common ratio of 2 does not satisfy the condition for convergence, which is -1 < r < 1.

Step-by-step explanation:

The question asks us to find the sum of an infinite geometric series. The given sequence is An = 18(2)^(n-1). For an infinite geometric series to have a sum, the common ratio r must satisfy -1 < r < 1. In this sequence, the common ratio is 2, as each term is 2 times the previous term. Since 2 does not satisfy -1 < r < 1, the series does not have a sum because it diverges. Therefore, we can conclude that the sum of the infinite geometric series related to the sequence An = 18(2)^(n-1) does not exist.

3 votes

Answer:

Step-by-step explanation:

Since r=2 and |r|>1 the sum does not converge to any value. The sum does not exist for this infinite geometric series.

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