Thread: Series - Converge or diverge

Hello,

How can I show if these series are convergent or divergent?

∑k = 1∞ ((k!)^(1/k))/(k)


For the following series:

∑k = 1∞ (e^(3ik))/(k^(3/2))

I have started a solution here:http://img819.imageshack.us/img819/6864/solution.jpg
and was wondering if it is correct. Why is (e^(3ik))=1 when k->∞


Appriciate any guidance and a detail explanation.

Thank you

because it's magnitude is 1.

Originally Posted by 4Math

Hello,

How can I show if these series are convergent or divergent?

∑k = 1∞ ((k!)^(1/k))/(k)


For the following series:

∑k = 1∞ (e^(3ik))/(k^(3/2))

I have started a solution here:http://img819.imageshack.us/img819/6864/solution.jpg
and was wondering if it is correct. Why is (e^(3ik))=1 when k->∞


Appriciate any guidance and a detail explanation.

Thank you

so

Originally Posted by simplependulum

so

Is this mean that the seies convergent or divergent??

Does converge or diverge?