SOLUTION: Find the sum of the infinite geometric series 64+48+36+27+...If it has one.

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Question 407934: Find the sum of the infinite geometric series 64+48+36+27+...If it has one.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
This sum is represented in sigma notation by 64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29.

If you know that an infinite geometric series sum%28ar%5Ei%2C+i+=+0%2C+infinity%29 converges if and only if -1+%3C+r+%3C+1, we conclude that the series converges to a%2F%281-r%29. Here, a+=+64 and r+=+2%2F3, so

64%2Asum%28%282%2F3%29%5Ei%2C+i+=+0%2C+infinity%29+=+64%2F%281+-+%282%2F3%29%29+=+192.