# Determine if the sum Converges or Diverges

1. Dec 4, 2011

### McAfee

1. The problem statement, all variables and given/known data

3. The attempt at a solution

1. I have no idea. I know that the summation of the series converges.

2. I think it would diverge because the limit of the function does not equal zero.

3. I have tried the ratio test and got 1. Can't use the alternating series test because when ignoring signs the function increases.

2. Dec 4, 2011

### Dick

For 3 what's the limit of (5n-1)/(n+5) and what does that tell you about convergence? For 1 I think they might be asking you to estimate the difference using an integral.

3. Dec 4, 2011

### hunt_mat

2) is correct
3) Think about the function $f(x)=\ln x$

Last edited: Dec 4, 2011
4. Dec 4, 2011

### McAfee

The limit of (5n-1)/(n+5) as x approaches infinity equals 5 thus meaning that the series in divergent? I think

5. Dec 4, 2011

### McAfee

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I'm not sure what [itex]f(x)=\ln x[/quote] means. Can you plus explain.

6. Dec 4, 2011

### Dick

Right. If the nth term of a series doesn't approach 0 then it's always divergent. Now can you write an integral that's greater than the difference in 1?