Question

Test the series for convergence or divergence. ∑from n=1 to ∞ ((n^3 -1)/(n^4+1))

Answer 1

I do the alternating seriestest. It shows that bn >0, (bn+1)<bn and the limit is 0. So, it is convergent but the correct answer is divergent. Why?

Answer 2

why alternating series? All the terms are positive.

lim(n->∞) a_(n+1)/(a_n) = n^3/n^4 = 1/n

The harmonic series diverges

Answer 3

Test the series for convergence or divergence.∑from n=1 to ∞ ((e^n) /n^2)

n = 1