Ratio test takes the infinite limit of: which simplifies to: . The series diverges because the infinite limit is greater than one.
This series section is really bugging me. Am I allowed to use the word friggin? I can't get an answer that makes sense for n!/100^n with the Riemann symbol in front. I try to use the Ratio Test and then realize that the terms are positive so I don't need an absolute value.
I do some algebraic manipulation and come up with ((n+1)/(101)^n)) I don't see how I can take a limit/simplify the denominator here. Do I divide everything by ((101)^n))? Or did I do something wrong along the way and I should be getting a different result where I can see if it is <1 (converges) >1 (diverges) or = 1 (inconclusive).
As an aside, and this doesn't necessarily constitute another problem (hence no new thread). When I'm given a series n/(ln n)^n, can I use the rules of ln in the denominator and get n/((n)(ln n)) so the n's cancel out and the rest is easy?
I don't see how my method would be breaking any rules in math. I just want to check if I'm not mistaken.
I haven't gotten to logarithms yet as my teacher requested that I review algebra. I don't see how you got the n+1 in the numerator. There needs to be a 1 added to the numerator when the n comes down from being an exponent to multiply the denominator?
and eventually dominates for any so the terms diverge, and so the series itself diverges.
(that is for large enough and so the terms are bounded below by a multiple of a geometric series with common ratio greater than 1)