Convergence test problem

[rir0302]

(converges or diverges?)

Not sure how to start

 

[pka]

View attachment 14372(converges or diverges?) Not sure how to start

If we suppose that \(\displaystyle a_n=\dfrac{33+(-1)^n}{n}\) does it follow that \(\displaystyle a_n\ge\frac{32}{n}~?\)
Can we use a comparison test?

 

[Steven G]

I personally like pka's method.
You can also think of a_n as 33/n + (-1)ⁿn. Does that help?

 

[lookagain]

You can also think of a_n as 33/n + (-1)ⁿn. Does that help?

You meant you can also think of a_n as 33/n + (-1)ⁿ/n.

 

[Deleted member 4993]

View attachment 14372
(converges or diverges?)

Not sure how to start

You know:

\(\displaystyle \sum_{n=1}^{\infty}\frac{1}{n}\)

diverges. Now look at the hints given to you....