Let Prove converges and find its sum. This shouldn't be too bad. Just a neat series. I started with:
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Originally Posted by galactus Let Prove converges and find its sum. This shouldn't be too bad. Just a neat series. I started with: 1. The series converges by the Aternating series test. 2. Abels theorem tells us that: If converges, then: Now: for Hence with just a bit of manipulation we conclude that: RonL
Hello Originally Posted by CaptainBlack 1. The series converges by the Aternating series test. 2. Abels theorem tells us that: If converges, then: Now: for Hence with just a bit of manipulation we conclude that: Isn't the series that Galactus has to study ?
Well done to all who attempted. Here is what I done. Starting where I left off: Now, for any integer , we get: Therefore, Now, if we let we can see that converges, and it has the sum Which, it would appear, is pretty much the same idea that Paul had.
See this.
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