a fun fractions problem!

Well, it’s been a million years since the last post, but I’ll spare any readers the doleful reasons.  I’m trying to figure out how to be self-disciplined with my writing and learning, so hopefully this summer sees many more posts.

But for now I thought I’d share a little problem that I saw today.  This summer I’m an adviser to a group of high school students who are taking college classes.   A student in a college algebra type course showed me this “bonus” question on the bottom of his quiz:

Find the sum, \frac{1}{2\cdot 3} + \frac{1}{3\cdot 4} +\frac{1}{4\cdot 5} + \cdots + \frac{1}{99\cdot 100} .

I won’t spoil your fun by posting a solution, but I encourage you to do so. I’m definitely interested in different solution methods on this one.


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One Response to a fun fractions problem!

  1. Bowen Kerins says:

    I was given a similar problem in high school on one of those math-teamy tests.

    Prove this identity: 1/(cos 0 cos 1) + 1/(cos 1 cos 2) + 1/(cos 2 cos 3) + … + 1/(cos 88 cos 89) =
    (cos 1) / (sin^2 1). [All angles are in degrees.]

    I didn’t get anywhere with it, but someone said -one word- to me after the test, and I knew what to do from there. [It’s still pretty hard.]

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