Define a sequence recursively by .

Given , show lim .

Note: It can easily be shown that so just assume this is given.

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- September 22nd 2009, 05:31 PMcgiulzShowing a sequence tends to infinity
Define a sequence recursively by .

Given , show lim .

Note: It can easily be shown that so just assume this is given. - September 23rd 2009, 01:32 AMpaweld
Let .

We have the following reccurence for sequence :

But for this sequence explicit formula can be easily obtained:

Because the sequence is not convergent. - September 23rd 2009, 07:09 PMcgiulz
Hey, sorry for the late response, thanks though.

So I can just assume and just say since,

for all ?