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Show that $$\frac{1}{1 \cdot 3} + \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \cdots = \frac{1}{2}.$$

I'm not exactly sure what to do here, it seems awfully similar to Zeno's paradox. If the series continues infinitely then each term is just going to get smaller and smaller.

Is this an example where I should be making a Riemann sum and then taking the limit which would end up being $1/2$?

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    The magic words are "telescoping series".2012-07-31
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    Thank you for the magic words, I really just needed a push in the right direction!2012-07-31
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    @JackThompson, co may be you should write your own an answer to this question?2012-07-31
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    The magic words **are** a push in the right direction. You are supposed to take the hint to look up the magic words and see how to use what you find to solve the problem. Or maybe you did that - it's not clear to me from what you've written.2012-08-01

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