Does the Series Converge or Diverge?

[I'm Awesome]

Homework Statement

Determine whether the infinite series converges or divergens. If it converges find its sum.
\sum^{∞}_{k=1} \frac{k-3}{k}

Homework Equations

The Attempt at a Solution

I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.


However, I'm not sure if I'm using the test for divergence right.

 

[sid9221]

I found the limit and realized that the limit is 1. So I said that the series converges by the test for divergence. And since it diverges I don't have to worry about finding a sum.

You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.

 

[I'm Awesome]

You are contradicting yourself. Do you think it converges or diverges ?

Hint: This series doesn't converge try and use a comparison test too see why.

Sorry, I ment to say that the series diverges by the test for divergence because the limit is not equal to 0.

 

[sid9221]

Yes, by the non null test is this is divergent as the limit is not equal to zero.