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- January 3rd 2008, 10:27 PMperashfind sum
- January 3rd 2008, 10:56 PMCaptainBlack
- January 3rd 2008, 10:58 PMjanvdl
- January 3rd 2008, 11:00 PMJhevon
- January 4th 2008, 02:10 AMCaptainBlack
- January 4th 2008, 02:35 AMwingless
- January 4th 2008, 02:45 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 - January 4th 2008, 02:47 AMPaulRS
- January 4th 2008, 03:08 AMSoroban
Hello, perash!

Quote:

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

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

Multiply by . . . . .

Subtract [2] from [1]: .

Hence, we have: . . . .

- January 4th 2008, 03:54 AMCaptainBlack
- January 4th 2008, 11:23 AMperash
This wonderful solution

thank you Soroban