Recent content by lilypetals

Homework Statement Find a power series representation for the function and determine the radius of convergence: f(x)=ln(5-x)Homework Equations Manipulate into the form 1/(1-x).The Attempt at a Solution I know how to do this with other functions, say, x/(9+x2)... It would convert to x/9 *...

Actually, I just found a (surprisingly) helpful hint in the small-print margin of my textbook: we write out the first few terms to determine a and r of the series. a1=1/4 a2=-3/16 a3=9/64 So the series becomes 1/4(-3/4)n-1, which is convergent, because r=-3/4, which is less than 1. And its...

Homework Statement Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. \sumn=1infinity (-3)n-1/4nHomework Equations A geometric series, \sumn=1infinity arn-1=a + ar + ar2 + ... is convergent if |r|< 1 and its sum is \sumn=1infinity arn-1 =...

Okay, I think I get it. Does this translate to other situations as well? Dividing/multiplying by infinity causes the quotient or the product to become 0?

0, right?

Homework Statement Determine whether the sequence converges or diverges. If it converges, find the limit. an = e1/n Homework Equations The limit laws, adapted for sequences. The Attempt at a Solution I have the solution; I was just wondering if someone might explain it to me. I...

Thank you!

Thank you all for all the advice! I feel a little less worried now. Since I'm shaking on problem-solving, I picked up the suggested book for the course which is also actually rather highly rated, containing tons of practice problems and in-depth solutions, and I signed up for the study group...

If I use the ratio test...|an+1/an|=|((-10)n+1/(n+1)!)/(-10)n/n!|=10/(n+1). So the limit as n goes to infinity of 10/(n+1) can be found by dividing by n, and taking the limit of the result. And the limit of n as it goes to infinity of (10/n)/(1+1/n)=0/(1+0)=0. Since this is less than one, the...

I guess that's the problem--I'm not even sure which series to consider. I know that if I guess that the given series converges, I need a larger series which also converges, and I can meet the criteria by making the denominator smaller or the numerator larger. It's hard to imagine making the...

Homework Statement \Sigma from n=0 to infinity (-10)n/n! Determine the absolute convergence, convergence, or divergence of the series. Homework Equations In this section, it's suggested that we use the following to determine a solution: A series is called absolutely convergent if the series...

Hello everyone. -waves- I'm new so...don't kill me or...anything like that, but y'all seem like nice people, what with the devoting-your-time-to-helping-with-homework questions thing. That's super cool of you. (: So, I have this scenario, and I'm looking for some advice. I failed my first...