Find the sum of this infinite series.

Question

anonymous · Answer

attachment

anonymous · Answer

=3^(1/n)

anonymous · Answer

Would this be a geometric series?

freckles · Answer

are you sure you are suppose to find the sum? Or determine if it converges or diverges?

anonymous · Answer

Well if it diverges or converges.

anonymous · Answer

How could you determine if it converges without finding the value?

freckles · Answer

there are tests you can perform

freckles · Answer

like root test, ratio test, and so on...

freckles · Answer

see what happens if you look at 
$$\lim_{n \rightarrow \infty} \sqrt[n]{3}$$

freckles · Answer

if this doesn't equal 0
you can certain say 
$$\sum_{n=1}^{\infty}\sqrt[n]{3}$$ diverges 

(this is my the divergence test)

freckles · Answer

that is only if that limit isn't 0

freckles · Answer

so let me know what you get for that limit

anonymous · Answer

1, which is not 0. Thus it is divergent.

anonymous · Answer

@freckles Why is this true though? How does this rule work?

anonymous · Answer

(I know this rule from learning it previously in class, but how does it work?)

amistre64 · Answer

can we sat u = 1/n ?

anonymous · Answer

state? sure

amistre64 · Answer

when n=1, u=1
when n=infinity, u = 0

maybe lol

freckles · Answer

http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx I don't know if paul explains it here or not but these are definitely my choice of notes for calculus

anonymous · Answer

Okay, I'll make sure to read those through @freckles

amistre64 · Answer

anonymous · Answer

:)