Question

series convergence

Answer 1

\[\sum_{n=1}^{\infty} \sqrt{\frac{ n+1 }{ 4n^{3}+1 }}\]

Answer 2

HI!!

Answer 3

the numerator has degree \(\frac{1}{2}\) and the denominator has degree \(\frac{3}{2}\) and since \[\frac{3}{2}-\frac{1}{2}=1\] this will not converge
the difference has to be larger than one
this is not an actual text mind you, it is just the answer

Answer 4

you no doubt need the comparison test, or the limit comparison test
compare to \(\sum\frac{1}{n}\)

Answer 5

ok using the comparison test this is how I broke it down\[\sqrt{\frac{ n }{ 4n^{3} }}=\sqrt{\frac{ 1 }{ 4n^{2} }}=\frac{ 1 }{ 2n }\]

Answer 6

then that's divergent so the other one would be divergent

Answer 7

@misty1212 would that be right?