Question

conditionally/absolutely convergent or divergent?
n=1 to infinity: cos(npi) / ((n+1)*ln(n+1))

Answer 1

first see what happens at n-->inf

Answer 2

to the denominator

Answer 3

hmm I see, it just increases to infinity right? and the numerator go between -1 and 1? but what next?

Answer 4

If the denominator of a rational expression grows arbitrarily large as some part of it (like a variable) approaches \(\infty\), then the whole rational expression approaches 0.