Series Convergence and Divergence

Luscinia
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Homework Statement


Determine if the following series converges or diverges. If it converges determine its sum.
Ʃ1/(i2-1) where the upper limit is n and the index i=2


Homework Equations



The General Formula for the partial sum was given:
Sn=Ʃ1/(i2-1)=3/4-1/(2n)-1/(2(n+1)

The Attempt at a Solution


I have no idea where to start. I tried to get the General Formula, but I am really confused as to how to even start. I tried to split the function with partial fractions and somehow got 1/(2(i+1))-1/(2(i-1))
 
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oops! I got it. It's a telescopic sum. I need to open my eyes a little more.
 
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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