calculus help!? Its for testing series for divergence and convergence.?

Question

I have a quiz on testing series for convergence and divergence and I just don't get the direct comparison test and the alternating series test. I just need some simple steps and/or some simple examples. that would be really helpful. thanks.

Answer 1

Here is a link to some great examples with layman's term explanations:

http://www.sosmath.com/calculus/improper/convdiv/convdiv.html

Answer 2

critical try can basically be used if ne^-n is a "function" that decreases for all values n>a million and continuous to infinity. so, ne^-n resembles xe^-x which equals x/(e^x). f(x) = x/(e^x) is continuous for all values x>a million with the help of searching at it good? to attempt to work out if that's lowering, locate the spinoff. utilizing the quotient rule, you get: (a million/e^x) - (x/e^x) Plug in a million for x to attempt. (those are approximations) .5 - .5 = 0 Plug in 2 .3 - .5 = -.2 The function does decrease so that you may be conscious the critical rule. If the critical of f(x) from a=a million to b=infinity dx diverges, then the sequence diverges. If it converges then it converges. Use the incorrect critical regulations.