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I'm trying to prove for every positive even number, $$x = 2y$$ that

$$\sum_{i=0}^y {x \choose 2i} 2^{2i} = \sum_{i=0}^{y-1} {x \choose 2i + 1}2^{2i+1} + 1$$

Also to find and prove a similar equation for odd positive numbers $$x = 2y+1$$

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    Please spell out positive-it is only four extra keystrokes and more common ones at that. Also, int as opposed to integer looks like a C data format to me.2012-09-18
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    sorry i'll fix that2012-09-18

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