I do not understand your "integral test"
You know that
Therefore there exists N such that for every n > N, or
And you know that the series converges
Another method is to calculate the limit of
i have to tell if this series is convergent or divergent, so i figured i could try the integral test here. the problem is, once i get to the stage of substituting with:
i get a little bit lost because integration really isn't my strong point >_<
i realize that after i have integrated i need to put it in limit form and evaluate it, i just can't get the integration part done. please help?
i just learned the integral test yesterday, it (apparently) says that if you have a positive, decreasing, & continuous function that you can replace your sequence with, you can use the improper integral of that, turn it into a limit, and if that converges, the sequence converges. if it diverges, the sequence diverges. (or so i was told)
edit:
& i don't really see why this is:
Therefore there exists N such that for every n > N, or
This becomes a whole lot easier if you write it as . Then integrate by parts, twice.
i get a little bit lost because integration really isn't my strong point >_<
i realize that after i have integrated i need to put it in limit form and evaluate it, i just can't get the integration part done. please help?
so, trying to integrate this by parts:
i first said
then i got
-e^-x*x^2- integral of -e^-x*2xdx
so i did parts again, with
=-e^-x*x^2+e^-x*2x+ integral of 2e^-xdx
=-e^-x*x^2+e^-x*2x-2xe^-x
i really feel like i'm doing something wrong,
can someone help?
p.s.- i apologize for the last few lines..LaTex was giving me some trouble >.<
oh, wow, that is a big difference then!
i see how it derives to a different thing, but, i don't know how to get it
thanks though!
also, getting back to the bigger question
i plugged the integrated version back into the limit from 3 to infinity
and i ended up with something like..
i figured the first part of that was going to go to zero because of the e^-infinity
does this mean that the integral converges, & thus, the series converges?
(sorry again, LaTex hates me)