Limit of a Series with Unknown Variable K

[K.QMUL]

Homework Statement

Determine whether the following are convergent, divergent or oscillating.

Homework Equations

Please see the attachment

The Attempt at a Solution

Please see the attachment. I am unsure about this as when I plot a graph without K its convergence

 

[pasmith]

You haven't applied the ratio test correctly. You have
$$\lim_{i \to \infty} \left|\frac{a_{i+1}}{a_i}\right| = \lim_{i \to \infty} \left(\frac{i + 1}{i}\right)^2 e^{-K}$$
which is correct. But then you don't try to find the limit, which is what you need to apply the ratio test.

 

[K.QMUL]

How would I go about finding the limit?

 

[dirk_mec1]

i+1~i.

 

[K.QMUL]

Mmmm.. still not sure, am I going about it in the right direction, does it seem divergent?

 

[Mark44]

Rather than guess whether the series is divergent or convergent, why don't you finish your work on the limit?

 

[K.QMUL]

I thought I had finished, is there something I am missing?

 

[dirk_mec1]

Can you find the limit of post #2?