Solution to May Problem

As I mentioned in the last post, at the end of the May meeting, Bob Sachs left us with the following problem:

Can you find a general formula for the following sum?
1 × 2 + 2 × 3 + 3 × 4 + … + n(n + 1)

I don’t know if we actually have a solution, but Margaret Coffey put a lot of effort into trying to find one! Her attempt at a solution is here:
https://novamtc.files.wordpress.com/2011/05/mathcircleproblem-mcoffey-110530.docx

Feel free to send me a file if you have a different approach, and I’ll post it. Or simply write up your thoughts as a reply to this post.

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