# Closer to One

Earlier this evening I was poking around map.mathshell.org looking for bite-sized middle school tasks. I found a limited but great set of questions here and was inspired to ask this:

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:

# The Question

Which is closer to 1? Does it depend on n? Explain.

# My Challenge

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.

# A Solution

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.)