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- Jan 3rd 2008, 11:27 PMperashfind sum
- Jan 3rd 2008, 11:56 PMCaptainBlack
- Jan 3rd 2008, 11:58 PMjanvdl
- Jan 4th 2008, 12:00 AMJhevon
- Jan 4th 2008, 03:10 AMCaptainBlack
- Jan 4th 2008, 03:35 AMwingless
- Jan 4th 2008, 03:45 AMPaulRS
Without differentiating

We want to find ( By the root test you can see that the series converges for )

Now we consider:

So: whenever (Because it is a geometric series)

Thus: and we obtain: :D - Jan 4th 2008, 03:47 AMPaulRS
- Jan 4th 2008, 04:08 AMSoroban
Hello, perash!

Quote:

We have: . . . . . . . . . .

Factor: . . . . . . . . . . .

Multiply by . . . . .

Subtract [2] from [1]: .

Hence, we have: . . . .

- Jan 4th 2008, 04:54 AMCaptainBlack
- Jan 4th 2008, 12:23 PMperash
This wonderful solution

thank you Soroban