I came across this problem that I couldn't really find an effective approach for. It was the simplification of $(i+1)^{2010} \text{ }- (i-1)^{2010}.$

I know that this roughly translates to $ (i^{2010} + i^{2019} + ... i + 1) \text{ }$ minus a similar expression, and I also know that the answer is $2^{1006}i$, but I just don't know any other steps that I could take.


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