1. Ratio Test

So I need to determine whether the following converges or diverges, using the ratio test:
series from n=1 to infinity of (n*ln(n))/(2^n)
I got it down to (1/2)((n+1)(ln(n+1)))/(n*ln(n)), and I'm stuck. Any hints? Did I mess up in the algebra?

2. Hello,

You just have to say that when x approaches infinite, ln(x+1)~ln(x)

And the limit of (n+1)/n can be found by dividing the numerator and the denominator by n.

So the limit of the ratio will be 1/2