Absolute & conditional convergence

[magnifik]

Homework Statement

Determine whether the series converges absolutely, conditionally, or not at all.

a) \Sigma (-1)ⁿn⁴/(x³ + 1)

b) \Sigma sin(x)/x²

Homework Equations

The Attempt at a Solution

a) positive series is n⁴/n³+1 .. do i do comparison test ??

b) |sin(x)|/x²
compare it with 1/x² which converges.. so it's absolutely convergent??

 

[Dick]

You are kind of freely mixing n's and x's here. Are they supposed to be the same? If so, for the first one ask whether the nth term goes to zero. For the second one, yes, it's absolutely convergent.

 

[magnifik]

woops, mixing up the n's & x's was a careless mistake

 

[magnifik]

for a) the positive series diverges because n^4/n^3 + 1 goes to infinity, but I'm not sure if the original series converges or diverges

 

[Dick]

for a) the positive series diverges because n^4/n^3 + 1 goes to infinity, but I'm not sure if the original series converges or diverges

A series whose terms don't go to zero diverges no matter what the signs on the terms. Look at the definition of convergence in terms of partial sums.