Which is closer to 1? Does it depend on n? Explain. (n-1)/n or n/(n-1) Inspired by Q2 on this: http://t.co/zUp670WyqS
— Michael Fenton (@mjfenton) April 23, 2014
Just in case Twitter messes up the formatting on whatever device you’re reading on, here’s the question again, as well as my challenge to you and a solution of my own:
Which is closer to 1? Does it depend on n? Explain.
I’m curious to know how others reason through and/or visualize this problem. If you find yourself with 5-10 spare minutes this week, scribble out an approach/solution/representation (or two) on a napkin, take a photo, and drop a link to the image in the comments. I’ll update this little ditty on Friday by embedding images in the post.
Pictures, words, algebra, numbers, proof with words, proof without words… It’s all fair game here.
Don’t peek until you’ve given it a go yourself (and hopefully shared your solution in the comments), but here’s my visual argument, sans words. (As in, “I’m not providing any words.” Let me know if you think it needs a comment to clarify.)