MATH SOLVE

4 months ago

Q:
# When will an infinite geometric series with β1 < r < 0 converge to a number less than the initial term? Explain your reasoning, and give an example to support your answer.

Accepted Solution

A:

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<r<0, an example with a1>0, such as 1000-100+10-1+...

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<r<0, an example with a1>0, such as 1000-100+10-1+...