Recent content by Randall

LCKurtz, no I had not read it when I was responding to Stephen, but I have read it since and have replied to you.

LCKurtz: Ok thanks I tried that but still had to use L'Hospital's rule to evaluate the limit as n goes to infinity. For Bn, I ended up with lim n to inf of 15 / 6n = 15/infinity = 0. So, since An = 0, I get a C of 0/0, which is undefined yes, or is C = 0? Thanks.

Hi Stephen: so when I used Bn = 0.5^n, and then analyzed it as n goes to infinity, I got Bn = 0. And, since I already determined that An=0, that makes my C = 0/0, which is undefined, yes? So I can't apply the limit comparison test for Bn being a convergent series.

Homework Statement Use the limit comparison test to prove convergence or divergence for the series sum from n=1 to infinity for ((5n^3)+1)/((2^n)((n^3)+n+1)) Homework Equations The limit comparison test says that if you have two positive series, sum An and sum Bn, let C=lim n to infinity of...

I'm not sure I understood Vela's hint. That seems to have it more complex :(

Thank you all - I use L'Hospital's rule and found the limit to be 2.

Homework Statement what is the lim as n goes to infinity of (ln(n+2))/(ln(2n)) ? Homework EquationsThe Attempt at a Solution It looks like you would get "small" infinity over "large" infinity, so does that make it 1? undefined? 0? thanks. Is there some simplifying I should be doing? Thanks.

Homework Statement Use the limit comparison test to show the series converges or diverges: Sum from n=1 to infinity of ((5n^3)+1)/((2^n)((n^3)+n+1)) Homework Equations suppose Sum An and Sum Bn are two positive series. Let lim as n goes to infinity of An/Bn = c: 1) if 0<c<inifinity then either...

Doesn't it converge to 1? 1 + 0 = 1? If not, why not? And also what should I choose instead to be bn? Thanks

Homework Statement Use the limit comparison test to check for convergence or divergence: Sum from n=1 to infinity of ((2n)^2+5)^-3 Homework Equations let lim n to infinity of An/Bn = c 1) if 0<c<infinity then either both converge or both diverge 2) if c=0 and sum Bn converges, so does sum An...

Thank you! Yes I used substitution and got it to work :)

Homework Statement Use the integral test to determine if this series converges or diverges: sum from n=1 to infinity of n/(1+(n^2)) Homework Equations Integral test: a series and it's improper integral both either converge or both diverge The Attempt at a Solution see attached - I need help...

Ahhhh. I see. This is simply the sum of two different geometric series - one with a ratio of 4/5 and one with a ratio of 3/5, yes? I feel silly now

Homework Statement Find the sum of the series from k=0 to infinity of ((4^k)-(3^k))/(5^k) Homework Equations I'm not sure exactly. I know the test for divergence is if lim n approaches infinity of the function from m=1 to infinity does not equal 0 then the series cannot diverge The Attempt...

I guess I'm not clear how to go about solving this problem then. Can you help me choose the correct procedure for finding the equation of the line tangent to the curve? Don't I have to take the derivative or something somehow? I'm not clear on what to do...