Question

Determine whether the series is convergent or divergent.

Answer 1

where is the series?

Answer 2

\[\sum_{n=1}^{\infty} (\frac{ 5 }{ n^4 }+\frac{ 4 }{ n \sqrt{n} } )\]

Answer 3

convergent \[1/n^{p} \] if p > 1 which in this case it is\[1/n^{4} and 1/n^{3/2}\]

Answer 4

I am sorry but I am not understanding

Answer 5

meh soz was in a bit of a rush ;)
\[\sum_{0}^{\infty} \frac{ 1}{ n^{p} } \]
is the P-series which is convergent for p>1 and divergent for p<1 or p=1

The series you wrote is just 1/n^4 + 1/n^(3/2)
and since both 1/n^4 and 1/n^(3/2) are convergent so is their sum
wanted to write it more technically but the equation menu kept bugging out so this will have to suffice :(

Answer 6

Thank you!!

Answer 7

np