Please refer to [this link](http://snap.stanford.edu/class/cs224w-readings/erdos59random.pdf). It is Erdos and Renyi's first paper on Random Graphs (1959). I am trying to work through it. 

I'm struggling with equations (16), (17) and (21).

(16)
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- I'm not sure why they are using those two bounds in the summation? It seems redundant
- Why they did not use the result from (15) in (16) in the summation. They only used (14)?

(17)
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- Why does loglog(n) replace M in (17)?

(21)
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- What does the (-1)^k figure do? Why is it necessary?