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IA Advice/Feedback

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Hey guys, 

So I was looking around for an IA topic (of couse i am), and I found something that was interesting to me. I watched a Numberphile video on the sum of all natural numbers, which would be -1/12. I was wondering if you guys had any advice on this, like if it is a good idea to explore or not, if it is doable, etc. Any feedback would be greatly appreciated.

Also, I am still a bit confused as to what exactly should we do for the IA, like do we have to prove something? Do we have to develop a new idea? I know we have to apply the math into a region, but could someone please give a little more detail? 

Thank you all so much!!

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