If the limit exists, find the limit of the sequence:

heres the equation: http://img402.imageshack.us/img402/5907/untitledav2.jpg

any help with this one please.

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- Jan 30th 2007, 03:44 PMrcmangofind the limit of the given sequence.
If the limit exists, find the limit of the sequence:

heres the equation: http://img402.imageshack.us/img402/5907/untitledav2.jpg

any help with this one please. - Jan 30th 2007, 05:08 PMThePerfectHacker
Observe the inequalities,

Thus,

Thus, multiply by ,

Now,

Thus, by the squeeze theorem,

- Jan 30th 2007, 07:29 PMrcmango
okay, i see that we used the squeeze theorem, however,

in the second part of 'Observe the inequalities' where it = n + ln2

why did we raise 1 to e^n?

also, we used 1/n for a bound in the squeeze theorem, is this because you recognized it as a series? if so, which one.

thanks for all the help! - Jan 30th 2007, 07:48 PMThePerfectHacker
- Jan 30th 2007, 10:15 PMrcmango
okay, i can see as both sides of the squeeze theorem converge to 1.

then, also the middle equation converges to 1.

thanks for your help.