How do you tell if a infinite geometric series has a finite sum

[From: ] [author: ] [Date: 13-03-06] [Hit: ]

-Since the common ratio 1/5 is between -1 and 1, it converges. The sum is 2/(1 - 1/5) = 5/2 or as you put it 2.5. Either the answer key is wrong, or you are misreading it.......

The equation is: 2+2/5+2/25+2/125+...
I thought the answers would be 2.5, but the correct answer is the series does not have a finite sum. Can someone explain to me why this is? Since it's converging I would think it does! 10 points to whoever can provide an explanation!

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Since the common ratio 1/5 is between -1 and 1, it converges. The sum is 2/(1 - 1/5) = 5/2 or as you put it 2.5. Either the answer key is wrong, or you are misreading it.

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