# convergence

1. ### How to solve two series to figure it out the convergence / divergence

Hello, guys! I have two series: \sum_{n=1}^{\infty}(-1)^{n}\dfrac{3n-1}{n^2 + n} My question is how to figure it out their convergence / divergence.
2. ### General Question about Convergence/Divergence Tests

Hi guys! I'm here again with a general question that's been bothering me all day today as I study for my calc 2 exam which is primarily on tests: I'm taking Calculus 2 for Physics/Engineers as part of my course curriculum for getting a Bachelors in Chemistry and I'm doing well in understanding...
3. ### Generalized Mediant. New root approximating methods

Allow me to introduce a very simple arithmetical operation: The Arithmonic Mean, which surprisingly and from the evidences at hand, has not been used in mathematics since ancient times up to now. I use the word 'Surprisingly', because it is a generalization of the 'Mediant' operation which is...
4. ### Series and Convergence Tests

Hi Guys, I would like to ask one question about a multiple choices that I kept getting wrong. Can someone shed some light?
5. ### Sequence Convergence Proof

Hi, I've been reading a book in order to prepare for a heavy on the proofs calculus course in the fall and have run into some trouble with the following proof Prove that the sequence $(a_n)$ given by $a_n = 3 - \frac{4}{n}$ $\forall n \in \mathbb{N}$ converges to 3. The final lines of the proof...
6. ### Interval of Convergence for differing odd/even coefficients of power series

Hello, I am studying for a midterm this week. One of the practice problems is to find the radius of convergence of \sum_{n=0}^{\infty} a_n x^n where a_n = 5^n if n is odd and a_n = 1/3^n if n is even. It took me a while to hazard a guess that I take the smaller of the two radii? Then a =...
7. ### convergence of integral

Investigate the convergence of the integral of ((sqr(2x/pi)-sin(x))^-1 from 1 to pi/2 thank's in advance http://www.wolframalpha.com/input/?i=compute+the+integral+of+(sqr(2x%2Fpi)-sin(x))%5E-1+from1to+pi%2F2
8. ### Indefinite integrals and convergence

Can somebody confirm if this is correct and also i need a little help with the convergence. I think i need to fiind p=Alpha*something. Sorry for bad handwriting Imgur: The most awesome images on the Internet
9. ### Proving a Sequence's Convergence

Hello, can you please check my work? Prove sin(n^2)/n^(1/3) converges to 0 Proof for any e > 0 abs(sin(n^2)/n^(1/3)) < e sin(n^2)/n^(1/3) < e Since the range of sin(n^2) is [-1,1], sin(n^2)/n^(1/3) < or = 1/n^(1/3) so let 1/n^(1/3) < e. So 1/n < e^3 let N < or = n Then, sin(n^2)^3/n < or =...
10. ### ratio test to test absolute convergence

in this question , i tried to solve it using ratio test to determine whether it is absolutely convergent or not , unfortunealy , i keep on getting infinity/ infinity , what does it mean ? does it mean diverge absolutely or ration test is not suitable to test the series ? if it is diverge...
11. ### Interval of Convergence of Infinite Series

Hi I have two questions asking me to find the interval of convergence of an infinite series: 1. Sum n=1 - infinity of: (2x)^n/(n^2+1); and 2. The Taylor series (or actually McLaurin series I think) for ln(1+x) about x=0 ie sum k=1 to infinity ((-1)^k*x^k)/k The actual words I have used are...
12. ### Series Convergence

Please show me how to do this. I think three converges because you can compare it to the convergent p- series 1/n^2 correct? What about I and II?