convergent or divergent

1. Improper integral (convergent/divergent)

Determine whether \int_{-\infty}^{\infty} xe^{-x^2}dx is convergent or divergent. Evaluate it if it is convergent. I tried using integration by parts, but failed to integrate e^{-x^2}.
2. Convergent/Divergent Series help!

I have a couple of Q's I'm stuck on help and help would be MUCH appreciated! I have to use either the limit comparison or the comparison test only - Sum (n=1 to infinity) n/(2^n) Sum (n=1 to infinity) 1/(2 + n^0.5)
3. Series - determine if this series is convergent/divergent

Hi, I need help with this series: from n=2 to infinity, n/[ln(n)]^n inf Σ ____n_____ n=2 [ln(n)]^n I tried the ratio test and when I went to take L'Hopital's I got into a big mess, can someone show me the solution? Thank-you!
4. Convergent/Divergent Integral

Evaluate the following integral if it is convergent. \int_1^{\infty}\frac{ln^2x}{x^3}dx
5. Following series convergent/divergent

Here are the 2 series where their nth terms are shown: c_n = (-1)^n \frac{(n+1)^n}{n^n} d_n = \frac{(n+1)^n}{n^{n + 1}} Attempted solution: So I know about all the tests: monotone convergence criterion, comparison test, root test, ratio test, and alternating series test. For c_n I...
6. Convergent/Divergent Integrals

For the following two problems, does the integral diverge or converge (if so, to what) Integral of sinx/(cosx - 1) from -pi/2 to pi/2 Integral of e^x/x from 1 to infinity Thanks!
7. convergent/divergent series

\sum_{k=0}^{\infty} \sqrt[n]2 -1 i'm supposed to test this series for convergence or divergence i just learned the root test (i'm assuming maybe i should use it here?) and i've reviewed the examples in my book but i'm not really sure how to apply it.. help please?
8. convergent/divergent series

test for convergence and/or divergence \sum_{n =1}^{\infty}n sin (1/n) is convergent? i'm not sure what to do when it comes to trig functions in series.. integral test? comparison test? (Speechless)
9. Series Convergent/Divergent

Determine whether the series \sum_{n=1}^{\infty} ln(n+\frac {1} {n} )- ln (n) converges or diverges. I'm really bad with series. (Speechless)
10. convergent/divergent integrals

Suppose f and g are continous functions with f(x)  g(x)  0 for x  a then (A) If integral a to infinity f(x) dx is convergent, then integral a to infinity g(x) dx is convergent (B) If integral a to infinity f(x) dx is divergent, then integral a to infinity g(x) dx is divergent (C) If...
11. in relation to convergent/divergent integrals

i was told that to be "convergent" an integral had to evaluate to a number but the question says "determine if convergent or divergent; if convergent, evaluate" so i'm just wondering..how does one determine if something is convergent WITHOUT evaluating it? is there something i'm missing?
12. convergent/divergent help

is this integral convergent or divergent? \int_1^\infty\frac{1}{x^2}\,dx
13. convergent/divergent help

Is this integral convergent or divergent? \int_0^\infty\frac{1}{x^2}\,dx
14. Help with convergent/divergent integral

Is this integral convergent or divergent? \int_0^\infty\frac{1}{\sqrt{x^2}}\,dx
15. Comparison Theorem and convergent/divergent

Use the Comparison Theorem to determine whether the integral is convergent or divergent. ∫_1^∞▒ x/√(1+x^6 ) dx
16. convergent/divergent problem help

Determine whether each integral is convergent or divergent. Evaluate those that are convergent. ∫_0^1▒ ln x/√x dx
17. convergent/divergent series

Hi, How to check whether \sum_{n=1}^{\infty}{n\sin}\frac{1}{n^3} is convergent/divergent? I could show that \sum_{n=1}^{\infty}{n\sin}\frac{1}{n^2} is divergent, but I don't know how to start with the first one... Won't someone drop a hint, please? Input appreciated. :)
18. B

Convergent/Divergent Series Help

Hi, I need to know how to prove the series: the sum from n=1 to infinity of (2n^2)/(n+3^n) convergent or divergent. I tried to do a limit comparison to (n^2)/(3^n) but I don't think that worked, so can someone else help? Thanks!
19. Convergent/Divergent Integrals

I'm asked to determine if the following integral is convergent/divergent: \int_0^1 \ln(x) dx So I'm just wondering if I'm on the right track with what I'm doing: \int_0^1 \ln(x) dx = \lim_{t \rightarrow 0} \int_t^1 \ln(x) dx As t \rightarrow 0 \Longrightarrow \ln(x) \rightarrow...
20. convergent/divergent

Determine whether the series is convergent or divergent. Sum from 2 to ∞ of 1/ [n(ln n)^.5]