Sigma - Revenge of the Exponents

Come Friday, a new POW. The title of it is Diminishing Squares

The Figure begins with a square of side length 2 units. Squares are continually added which have a side length which is one-half the previous square. Suppose this process continues to infinity. What is the area of the Figure? Explain your answer.

Well, the answer is most definitely not infinite, certainly not 5 and definitely not 6. Depending how far one wants to take this, it can involve some calculus, or just some simple arithmetic, but either way, it will involve plenty of exponents. Well anyway, if you give up, the answer can be found here ( a rough draft of my report )

Now for something more enfuriating. Battle of the Bands, which was scheduled for 1800-2200, yesterday was cancelled due to a tyrannical Principle. In our school, we have this annoying little thing called AI. Anyone who is on AI cannot participate in extra-curricular school events. Battle of the Bands is not a school event—In fact, the only association it has with the school is that it was scheduled to be in the auditorium. The insane principle went as far as to call an outside agency that was sponsoring it and tell them it was cancelled. Thats right!!! He wasn’t even running it, but he decided to make the called. If this was something like talent show, which is school run, then this would be ok, but they were paying to rent the auditorium and everything!!!! Talk about over using your power….

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