Question

Help Pleeasease

Answer 1

whats the question

Answer 2

0123456789

Answer 3

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

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?

Answer 4

@zepdrix @mathmate

Answer 5

@itz_sid
What is the question? Check convergence?

Answer 6

Determine whether it is Divergent or Convergent

Answer 7

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.

Answer 8

Oh I see. okay thanks!

Answer 9

You're welcome! :)

Answer 10

:D