$$\sum_{n=1}^{\infty}\frac{ n }{ 5n^3 +2}$$

For a problem like this, I dont need to use Integral test right?
I can just check the sequence?
$$\sum_{n=1}^{\infty} \frac{ n }{ 5n^3+2 } = \frac{ \frac{ n }{ n } }{ \frac{ 5n^3 }{ n } +\frac{ 2 }{ n }}=\frac{ 1 }{ 5n^2 }$$

And the sequence approaches 0, which can also be verified through P-series? Amiright?

Question

$$\sum_{n=1}^{\infty}\frac{ n }{ 5n^3 +2}$$

For a problem like this, I dont need to use Integral test right?
I can just check the sequence?
$$\sum_{n=1}^{\infty} \frac{ n }{ 5n^3+2 } = \frac{ \frac{ n }{ n } }{ \frac{ 5n^3 }{ n } +\frac{ 2 }{ n }}=\frac{ 1 }{ 5n^2 }$$

And the sequence approaches 0, which can also be verified through P-series? Amiright?

Champion · Answer

What is the question?  Check convergence?

HelpMePlz · Answer

Determine whether it is Divergent or Convergent

Champion · Answer

For convergence, you can compare term by term with n/5n^2.
Each term is smaller of n/(5n^3+2) is smaller than n/5n^3
Since n/5n^3=1/5n^2 is convergent absolutely, so will the given series.

HelpMePlz · Answer

Oh I see. okay thanks!

Champion · Answer

welcome ^_^