determine whether the series converges or diverges n=1 to infinity of (n+ln x)/(n^3+n+1)

Question

anonymous · Answer

using the comparison or limit test

anonymous · Answer

really confused on whether you would set bn as =n / n^3 or 1/n^3

hartnn · Answer

@amistre64

amistre64 · Answer

n controls the top i believe, so lets try n/n^3

anonymous · Answer

so i get lim as n approaches infinity (n^4 + n ln n) /( n^4+n^2 + n )

anonymous · Answer

= 1 so it converges?

amistre64 · Answer

well, it does converge :)

amistre64 · Answer

is the sum of 1/n^2  greater than the original sum?

how would you test that out?

anonymous · Answer

no it does not converge i believe in wolfram the answer seems to be diverges

amistre64 · Answer

anonymous · Answer

anonymous · Answer

oops that was another problem but similar style

amistre64 · Answer

amistre64 · Answer

if 1/n^2 converges, than by default since it is bigger .... the other one has to

anonymous · Answer

also converge i see

anonymous · Answer

anonymous · Answer

would you set b as 1/n^(3/2)

amistre64 · Answer

amistre64 · Answer

not sure how you picked ^3/2 .... but then im a bit rusty

anonymous · Answer

the initial problem was this|dw:1363208270574:dw|