determine whether the series converges or diverges

help?(Speechless)

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- Mar 21st 2009, 08:29 PMbuttonbearseries with factorial

determine whether the series converges or diverges

help?(Speechless) - Mar 22nd 2009, 06:34 AMSoroban
Hello, buttonbear!

Without the Ratio Test, I'm not sure of the proof.

Quote:

. Determine whether the series converges or diverges

. .

Divide top and bottom of the fraction by

Therefore: .

. . and the series converges.

- Mar 22nd 2009, 10:22 AMo_O
For all , we have:

So by comparison ... - Mar 22nd 2009, 04:35 PMbuttonbear
i'm sorry, i just didn't fully understand your post..

- Mar 22nd 2009, 06:23 PMo_O
I've showed that:

Since is convergent, by the comparison test ... what can you conclude? - Mar 22nd 2009, 06:44 PMbuttonbear
i can conclude that... because the larger sequence converges..the other one does too?

- Mar 22nd 2009, 07:04 PMbuttonbear
i'm just kind of confused as how to how you knew to pick for your larger sequence? or can it be any larger sequence?

- Aug 13th 2009, 03:28 PMjohntuan
sorry for bumping up an old thread but how did you know to compare it to 2/n^2 as opposed to 1/n^2??

- Aug 13th 2009, 03:39 PMjohntuan
oh nvm i think i see it, because you cant use 1/n^2, you can only use 2/n^2, cause if you only use the first term it would be 1/n, which is divergent according to the p-series, and so you use n>=2..ahh i see it..