Infinite Series Convergence using Comparison Test

titasB
Messages
14
Reaction score
2

Homework Statement



Determine whether the series is converging or diverging

Homework Equations




∑ 1 / (3n +cos2(n))
n=1

The Attempt at a Solution



I used The Comparison Test, I'm just not sure I'm right. Here's what I've got:

The dominant term in the denominator is is 3n and
cos2(n) alternates between 0 and 1

so,

1 / (3n +cos2(n)) < 1 / 3n

which is convergent geometric series, since | r | = 1/3 < 1

And so, 1 / (3n +cos2(n)) is convergent according to the Comparison Test
 
Physics news on Phys.org
looks ok to me. actually maybe you should change < to ≤ for when cos2 is zero
 
Last edited:
  • Like
Likes titasB
Thanks. Wasn't sure about the cos2(n) part
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
Back
Top