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Does the following infinite series have a sum or not and does it converge or diverge?

7-21+63-189+

User T Mitchell
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1 Answer

4 votes

Answer:

Explanation:

Please present these numbers as a list: 7, -21, 63, -189, ....

Otherwise it appears that you are adding them up, which is not the case.

We can tell that this is a geometric series because each new number is -3 times the previous number: -3(7) = -21, -3(-21) = 63, and so on. Let r = -3 and a = first number = 7.

a

The sum of an infinite geometric series exists if and only if |r} < 1. Here, |-3|, or 3, so in this case the sum of the series does not exist. That is, the series diverges.

User Jeyavel
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