Question

determine the series 4/square root of ((K^3)+1) converge or not? thx

Answer 1

\[\sum_{k=1}^{\infty}4/\sqrt{k ^{3}+1}\]

Answer 2

it converges to 0 ( because \[ \lim_{k \rightarrow +\infty } (4/\sqrt{k+1}^{3}) = 0\]

Answer 3

how can it converge to zero? all the terms are positive

Answer 4

it does converge though

Answer 5

idea is the degree of the denominator is bigger than 1
ok it is not a polynomial but
\[\sqrt{k^3}=k^{\frac{3}{2}}\] and
\[\frac{3}{2}>1\] so converges
probably use comparison test