Limit of an Arithmetic Series: Solving for the Limit as n Approaches Infinity

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Limn→∞ (n2/1+5+9+...+(4n-3))
 
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Since you apparently didn't take VietDao's suggestion, I'll tell you the answer is 1/2 and let you figure out if it's correct or not.
 
I have no idea how to do it...so I am asking to give me a clue to this problem!
 
The denominator is an arithmetic series, which sums to 2n2 - n. Therefore the limit is 1/2.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

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...
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