Question

Is the summation of 1/sqrt(n^3 + 1) , from 1 to infinity, convergent?

Answer 1

yup

Answer 2

oh this was not a yes or no question was it? it is yes converges

Answer 3

quick eyeball check says
\[\sqrt{n^3}=n^{\frac{3}{2}}\] and since
\[\frac{3}{2}>1\] you win

Answer 4

you want a test? integral test might do it but i think even comparison test works. compare to what i wrote

Answer 5

Just to clarify. Should I compare \[1/\sqrt{n^3 + 1}\] with \[1/\sqrt{n^3}\] ??

Answer 6

why not?

Answer 7

what is a 1 between friends?

Answer 8

So I'm comparing it with something divergent (by P-Series)? o.O

Answer 9

how pedantic do you want to be? you could use the integral test, which would involve showing
\[\int_1^{\infty}\frac{1}{\sqrt{x^3+1}}dx\] was finite,but this integral is a drad

Answer 10

oh no p series converges if p> 1 right?

Answer 11

\[\sum\frac{1}{n^p}\] is finite if p > 1

Answer 12

Ok. I got mixed up with 3/2 and 2/3. Thanks. xD