A Metric Space is just a set with a metric (a distance equation relating two points) defined on it that has certain properties. (Wikipedia actually isn't horrible for learning definitions of things, but I agree with your comment. But in this case it isn't horrible. Some of the examples are...
I was thinking about a new set of algorithms that could help. Say you have f2l solved except one of the edges is flipped. Instead of fixing it, what if we had algorithms that could solve OLL and flip the edge too. I know the algorithms could be nasty, but this would shave off a few seconds.
I play in the summer with my friends, but in college I never play because I am not trying to look like that big of a nerd haha. I have put together a mill that is hilarious to play with and then I have a red/green dragon deck that basically is mana ramp with green into big dragons. We don't...
I started cubing in march 2010. I got down to 30 seconds in that summer I think. I got down to 20 seconds at the beginning of the summer of 2011. A couple weeks ago I got a sub 15 ao100 but I don't know if I can repeat that right now.
Probably just look at it and look for a pattern? I am not sure what you are asking.
I guess you would look at what each of the terms of the sequence of partial sums is. So look at the sequence of the finite sum of n^2.
1, 5, 14, 30, 55, 91, etc.
Then you could find a function that describes...
mathematical induction on n.
here is an outline of what induction is:
There are two steps.
1. Prove that the base case works.
2. Assume that is works for the nth term. so what you have above. Then you want to show that it works for n+1.
So for your problem, 1^2 = 1= 1(1+1)(2*1+1)/6 = 1. So...