Determine if the sum Converges or Diverges

[McAfee]

Homework Statement

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.

 

[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.

 

[hunt_mat]

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

 

[McAfee]

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.

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

 

[McAfee]

2) is correct
3) Think about the function [itex]f(x)=\ln x

[/QUOTE]

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

 

[Dick]

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

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?