SOLUTION: Find the sum of the following infinite geometric series, if it exists. 1.02 + 2.04 + 4.08 + 8.16 +…

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Question 399240: Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +…
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
This is equal to

1.02(1 + 2 + 4 + ...), or %281.02%29sum%282%5Ei%2C+i+=+0%2C+infinity%29 in sigma form. However the series sum%282%5Ei%2C+i+=+0%2C+infinity%29 diverges, so the infinite sum diverges.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
You can also use the fact that if a series of (positive) terms sum%28a%5Bn%5D%2C+n+=+1%2C+infinity%29 converges, then the general term lim%28+x-%3Einfinity%2C+a%5Bn%5D%29+=+0 . By contraposition, since the general term a%5Bn%5D approaches infinity, the series itself diverges.