let's go from the beginning
1. problem
what the criteria for testing convergence do you know? (if u know any try applying it and if u have problem say where )
Hi All,
I took my time to scan these 7 problems from the book to see if you guys can help me out with any of them. I've missed about a week of class due to work travel, and it would really help if you guys can help me with the solutions, as I have a test in 4 days and need to know how to do these.
http://modernvirtual.com/1.png
http://modernvirtual.com/2.png
Thanks in advance!
I honestly don't know even where to start with these. I've missed about five days of a 3 hour class, so that was a lot of material. I tried to look up the material online and tried wolfram alpha as well as trying a few methods by hand and still cannot even comprehend how to do these.
u have D'alamberth (sorry if i mistype his name)
then :
so u have a cases :
or Rabel's (again sorry for mistyping)
or u can do it "by definition"
definition say that series converges or diverges if
is number then converges
if infinity nuber or doesn't exist it diverges
is array of partial sums
first of all those criteria that I wrote there isn't only them.... there are few more
as 3. problem i'm trying to google translate it (sorry if i understand what's point i'll post it )
for 5. problem i think is something to do with "Štolc" theorem (i think is something like "Shtolch" or )
he says that :
"if and arbitrary real sequences such that a sequence satisfies:
1° monotonically increasing
2°
if exist :
then exist and
and they are equal
i think that's it
hehehe or u can (i think again ) for #5 just (to se if is increasing or decreasing) just put and if it's true then is increasing but if then is decreasing (we do it like that here )