When will an infinite geometric series with - 1 < r < 0 converge to a number less than the initial term? Explain your reasoning, and give an example to support your answer.

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Mathematics

Delacruz

1 February, 23:37

When will an infinite geometric series with - 1 < r < 0 converge to a number less than the initial term? Explain your reasoning, and give an example to support your answer.

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Joel Davenport · Answer 1

If r is negative, the denominator of the formula for the sum of the series is positive and greater than 1.

If the initial term is divided by a positive number greater than 1, the result is a number smaller than the initial term.

So, if the initial term is positive, then the series will converge to a number less than the initial term. For - 1